Method and Apparatus of Quantizing Coefficients for Matrix-Based Intra Prediction Technique

ABSTRACT

A method of intra prediction of a block, comprising obtaining two lines of reconstructed neighboring samples; deriving a set of reference samples based on the two lines of reconstructed neighboring samples; obtaining a set of MIP coefficients based on a intra prediction mode obtained from a bitstream, wherein a MIP coefficient C MIP  of the set of MIP coefficients is obtained based on C MIP =v sgn ·(q&lt;&lt;s), where q is a magnitude of the MIP coefficient, wherein s is a left shift value and v sgn  is a sign value of the MIP coefficient; and obtaining a prediction block based on the set of reference samples and the set of MIP coefficients, wherein a reconstruct picture is obtained based on the prediction block.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of International PatentApplication PCT/RU2020/050058, filed on Mar. 24, 2020, which claimspriority of U.S. Provisional Patent Application No. 62/822,986, filed onMar. 24, 2019 and which claims priority to International PatentApplication No. PCT/RU2019/000442, filed on Jun. 21, 2019. Thedisclosures of the aforementioned patent applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

Embodiments of the present disclosure generally relate to the field ofpicture processing and to methods of intra prediction in video coding,and to the mechanism of signaling intra prediction modes.

BACKGROUND

Video coding (video encoding and decoding) is used in a wide range ofdigital video applications, for example broadcast digital TV, videotransmission over internet and mobile networks, real-time conversationalapplications such as video chat, video conferencing, Digital Video Disc(DVD) and Blu-ray® discs, video content acquisition and editing systems,and camcorders of security applications.

The amount of video data needed to depict even a relatively short videocan be substantial, which may result in difficulties when the data is tobe streamed or otherwise communicated across a communications networkwith limited bandwidth capacity. Thus, video data is generallycompressed before being communicated across modern daytelecommunications networks. The size of a video could also be an issuewhen the video is stored on a storage device because memory resourcesmay be limited. Video compression devices often use software and/orhardware at the source to code the video data prior to transmission orstorage, thereby decreasing the quantity of data needed to representdigital video images. The compressed data is then received at thedestination by a video decompression device that decodes the video data.With limited network resources and ever-increasing demands of highervideo quality, improved compression and decompression techniques thatimprove compression ratio with little to no sacrifice in picture qualityare desirable.

SUMMARY

Embodiments of the present disclosure provide apparatuses and methodsfor encoding and decoding based on the independent claims.

The foregoing and other objects are achieved by the subject matter ofthe independent claims. Further implementation forms are apparent fromthe dependent claims, the description and the figures.

The present disclosure provides a method of intra prediction, whereinthe method of the intra prediction is either a directional intraprediction method or an affine linear weighted intra prediction (ALWIP)method, wherein the method comprises the following steps. Preparing aset of reference samples. In case the method of intra prediction for afirst block is directional intra prediction, the method includesobtaining a first predicted signal of the first block of a first pictureby convolving the set of reference samples with a first set ofcoefficients; obtaining a first reconstructed block of the first picturebased on the first predicted signal. In case the method of intraprediction of a second block is ALWIP, the method includes obtaining asecond predicted signal of the second block of a second picture byconvolving the set of reference samples with a second set ofcoefficients, wherein the second set of coefficients comprisescoefficients of a core matrix A of ALWIP, and the coefficients of thecore matrix A and the first set of coefficients have same precision;upsampling the second predicted signal; and obtaining a secondreconstructed block of the second picture based on the upsampled secondpredicted signal.

Thus, the present disclosure proposes a unified directional intraprediction with ALWIP by aligning accuracy of multiplication operations.This unification enables a possibility to have a unified convolutionstep for the both methods and thus to eliminate hardware redundancy.

Each of the steps mentioned above includes parameters that may beadjusted. By defining a set of parameters, the sequence of steps mayoperate as ALWIP or as directional intra prediction. ALWIP, may also bereferred to as matrix-based intra prediction (MIP).

In the method, as described above, the first set of coefficients and/orthe second set of coefficients may be defined adaptively per position ofthe predicted sample, respectively.

In the method as described above, the coefficients of the core matrix Amay have a 6-bit precision such that 10-bit samples processing fits in16-bit arithmetic.

In the method as described above, the step of upsampling may be skippedfor directional intra prediction.

In the method as described above, the method may further compriseobtaining two lines of reconstructed neighboring samples; deriving theset of reference samples based on the two lines of reconstructedneighboring samples; obtaining a set of matrix-based intra prediction(MIP) coefficients based on an intra prediction mode obtained from abitstream, wherein an MIP coefficient C_(MIP) of the set of MIPcoefficients may be obtained using the following equation:C_(MIP)=v_(sgn)·(q<<s), where q is a magnitude of the MIP coefficient; sis a left shift value; v_(sgn) is a sign value of the MIP coefficient;obtaining a prediction block based on the set of reference samples andthe set of MIP coefficients; wherein a reconstructed picture may beobtained based on the prediction block.

In the method as describe above, obtaining a prediction block based onthe set of reference samples and the set of MIP coefficients maycomprise a matrix multiplication of the reference samples and the set ofMIP coefficients, wherein the multiplication operation in matrixmultiplication may be performed with reduced bit depth by repositioningshift operation after multiplication: p·C_(MIP)=v_(sgn)·((p·q)<<s),where q is a magnitude of the MIP coefficient; s is a left shift value;v_(sgn) is a sign value of the MIP coefficient; p is a reference sample,p=bdry_(red) ^(top)[i]0≤i<W; or p=bdry_(red) ^(left)[i], 0≤i<H.

In the method as describe above, the magnitude of the MIP coefficient qmay be a 6-bit depth value.

In the method as described above, the left shift value may be a 2-bitdepth value.

In the method as described above, multiplication may be performed by themeans of the multiplier that used in intra-interpolation process ofangular intra prediction.

The present disclosure further provides an encoder comprising processingcircuitry for carrying out the method as described above.

The present disclosure further provides a decoder comprising processingcircuitry for carrying out the method as described above.

The present disclosure further provides a computer program productcomprising a program code for performing the method as described above.

The present disclosure further provides a decoder, comprising one ormore processors; and a non-transitory computer-readable storage mediumcoupled to the processors and storing programming for execution by theprocessors, wherein the programming, when executed by the processors,configures the decoder to carry out the method as described above.

The present disclosure further provides an encoder, comprising one ormore processors; and a non-transitory computer-readable storage mediumcoupled to the processors and storing programming for execution by theprocessors, wherein the programming, when executed by the processors,configures the encoder to carry out the method as described above.

The present disclosure further provides an encoder, comprising apreparing unit configured to prepare a set of reference samples; a firstobtaining unit configured to, in case a first block is intra-predictedby directional intra prediction, obtain a first predicted signal of thefirst block of the first picture by convolving the set of referencesamples with a first set of coefficients, and obtain a firstreconstructed block of the first picture based on the first predictedsignal; a second obtaining unit configured to, in case a second block ofa second picture is intra-predicted by ALWIP, obtain a second predictedsignal of the second block of the second picture by convolving the setof reference samples with a second set of coefficients, wherein thesecond set of coefficients comprises coefficients of a core matrix A ofALWIP, and the coefficients of the core matrix A and the first set ofcoefficients have same precision; upsampling the second predictedsignal; and obtaining a second reconstructed block of the second picturebased on the upsampled second predicted signal.

In the encoder as described above, the first set of coefficients and/orthe second set of coefficients may be defined adaptively per position ofthe predicted sample, respectively.

In the encoder as described above, the coefficients of the core matrix Amay have a 6-bit precision such that 10-bit samples processing fits in16-bit arithmetic.

In the encoder as described above, the second obtaining unit isconfigured to skip the step of upsampling for directional intraprediction.

The encoder as described above may further comprise a third obtainingunit configured to obtain two lines of reconstructed neighboringsamples; a deriving unit configured to derive the set of referencesamples based on the two lines of reconstructed neighboring samples; afourth obtaining unit configured to obtain a set of MIP coefficientsbased on an intra prediction mode obtained from a bitstream, wherein anMIP coefficient C_(MIP) of the set of MIP coefficients may be obtainedusing the following equation C_(MIP)=v_(sgn)·(q<<s), where q is amagnitude of the MIP coefficient; s is a left shift value; v_(sgn) is asign value of the MIP coefficient; a predicting unit configured toobtain a prediction block based on the set of reference samples and theset of MIP coefficients; wherein a reconstructed picture may be obtainedbased on the prediction block.

In the encoder as described above, the predicting unit may be configuredto obtain the prediction block based on a matrix multiplication of thereference samples and the set of MIP coefficients, wherein themultiplication operation in matrix multiplication may be performed withreduced bit depth by repositioning shift operation after multiplicationbased on p·C_(MIP)=v_(sgn)·((p·q)<<s), where q is a magnitude of the MIPcoefficient; s is a left shift value; v_(sgn) is a sign value of the MIPcoefficient; p is a reference sample, p=bdry_(red) ^(top)[i] 0≤i<W; orp=bdry_(red) ^(left)[i], 0≤i<H.

In the encoder as described above, the magnitude of the MIP coefficientq may be a 6-bit depth value.

In the encoder as described above the left shift value may be a 2-bitdepth value.

In the encoder as described above, multiplication may be performed bythe means of the multiplier that used in intra-interpolation process ofangular intra prediction.

The present disclosure further provides a decoder, comprising apreparing unit configured to prepare a set of reference samples; a firstobtaining unit configured to, in case a first block is intra-predictedby directional intra prediction, obtain a first predicted signal of thefirst block of the first picture by convolving the set of referencesamples with a first set of coefficients, and obtain a firstreconstructed block of the first picture based on the first predictedsignal; a second obtaining unit configured to, in case a second block ofa second picture is intra-predicted by ALWIP, obtain a second predictedsignal of the second block of the second picture by convolving the setof reference samples with a second set of coefficients, wherein thesecond set of coefficients comprises coefficients of a core matrix A ofALWIP, and the coefficients of the core matrix A and the first set ofcoefficients have same precision; upsampling the second predictedsignal; and obtaining a second reconstructed block of the second picturebased on the upsampled second predicted signal.

In the decoder as described above, the first set of coefficients and/orthe second set of coefficients may be defined adaptively per position ofthe predicted sample, respectively.

In the decoder as described above, the coefficients of the core matrix Amay have a 6-bit precision such that 10-bit samples processing fits in16-bit arithmetic.

In the decoder as described above, the second obtaining unit (3005) maybe configured to skip the step of upsampling for directional intraprediction.

The decoder as described above, may further comprise a third obtainingunit configured to obtain two lines of reconstructed neighboringsamples; a deriving unit configured to derive the set of referencesamples based on the two lines of reconstructed neighboring samples; afourth obtaining unit configured obtaining a set of MIP coefficientsbased on an intra prediction mode obtained from a bitstream, wherein anMIP coefficient C_(MIP) of the set of MIP coefficients may be obtainedusing the following equation C_(MIP)=v_(sgn)·(q<<s), where q is amagnitude of the MIP coefficient; s is a left shift value; v_(sgn) is asign value of the MIP coefficient; a predicting unit configured toobtain a prediction block based on the set of reference samples and theset of MIP coefficients; wherein a reconstructed picture may be obtainedbased on the prediction block.

In the decoder as described above, the predicting unit may be configuredto obtain the prediction block based on a matrix multiplication of thereference samples and the set of MIP coefficients, wherein themultiplication operation in matrix multiplication is performed withreduced bit depth by repositioning shift operation after multiplicationbased on p·C_(MIP)=v_(sgn)·(q·q)<<s), where q is a magnitude of the MIPcoefficient; s is a left shift value; v_(sgn) is a sign value of the MIPcoefficient; p is a reference sample, p=bdry_(red) ^(top)[i] 0≤i<W; orp=bdry_(red) ^(left)[i], 0≤i<H.

In the decoder as described above, the magnitude of the MIP coefficientq may be a 6-bit depth value.

In the decoder as described above, the left shift value may be a 2-bitdepth value.

In the decoder as described above, wherein multiplication is performedby the means of the multiplier that used in intra-interpolation processof angular intra prediction.

In the encoder and the decoder as described above, the first and secondobtaining units may be the same.

It should be noticed, that MIP may be using a dedicated MPM signalingmechanism, as well as a redefined MPM list derivation mechanism, thatmay be enabled when intra_lwip_flag is 1.

The present disclosure reduces the number of checks in the parsingprocess by unifying the cases of signaling when intra_lwip_flag is 0 andwhen intra_lwip_flag is 1.

Based on a first aspect, the present disclosure relates to a method ofunification of MIP M list construction and consequently, a newdependency between the number of signaled directional intra predictionmodes and the size of the intra-predicted block.

Based on a second aspect, the present disclosure relates to an apparatusfor decoding a video stream includes a processor and a memory. Thememory is storing instructions that cause the processor to perform themethod based on the first aspect.

Based on a third aspect, the present disclosure relates to an apparatusfor encoding a video stream includes a processor and a memory. Thememory is storing instructions that cause the processor to perform themethod based on the second aspect.

Based on a fourth aspect, a computer-readable storage medium havingstored thereon instructions that when executed cause one or moreprocessors configured to code video data is proposed. The instructionscause the one or more processors to perform a method based on the firstor second aspect or any possible embodiment of the first or secondaspect.

Based on a fifth aspect, the present disclosure relates to a computerprogram comprising program code for performing the method based on thefirst or second aspect or any possible embodiment of the first or secondaspect when executed on a computer.

Details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features, objects, andadvantages will be apparent from the description, drawings, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following embodiments of the present disclosure are described inmore detail with reference to the attached figures and drawings, inwhich:

FIG. 1A is a block diagram showing an example of a video coding systemconfigured to implement embodiments of the present disclosure;

FIG. 1B is a block diagram showing another example of a video codingsystem configured to implement embodiments of the present disclosure;

FIG. 2 is a block diagram showing an example of a video encoderconfigured to implement embodiments of the present disclosure;

FIG. 3 is a block diagram showing an example structure of a videodecoder configured to implement embodiments of the present disclosure;

FIG. 4 is a block diagram illustrating an example of an encodingapparatus or a decoding apparatus;

FIG. 5 is a block diagram illustrating another example of an encodingapparatus or a decoding apparatus;

FIG. 6 is a drawing showing angular intra prediction directions and theassociated intra-prediction modes in Versatile Video Coding;

FIG. 7 is a simplified block diagram illustrating the method ofmatrix-based intra prediction (MIP) that is also referred to as affinelinear weighted intra prediction (ALWIP);

FIG. 8 is a detailed block diagram illustrating the method ofmatrix-based intra prediction (MIP) that is also referred to as affinelinear weighted intra prediction (ALWIP);

FIG. 9 shows MIP coefficients having a length of 10 bits including 9-bitmagnitude and a sign (1 bit);

FIG. 10 shows 6-bit magnitudes of MIP coefficients that are extractedfrom a 9-bit magnitude subject to the position of a non-zero mostsignificant bit (MSB);

FIG. 11 shows a representation of an MIP coefficient with a 6-bitmagnitude;

FIG. 12 illustrates how to reuse multipliers for intra-predictioninterpolation filtering by MIP;

FIG. 13 illustrates a flowchart of an embodiment of the presentdisclosure of a method of intra prediction, the method of the intraprediction being either a directional intra prediction method or anALWIP method;

FIG. 14 illustrates an encoder according to an embodiment of the presentdisclosure;

FIG. 15 illustrates a decoder according to an embodiment of the presentdisclosure.

In the following identical reference signs refer to identical or atleast functionally equivalent features if not explicitly specifiedotherwise.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following description, reference is made to the accompanyingfigures, which form part of the disclosure, and which show, by way ofillustration, aspects of embodiments of the present disclosure oraspects in which embodiments of the present disclosure may be used. Itis understood that embodiments of the present disclosure may be used inother aspects and comprise structural or logical changes not depicted inthe figures. The following detailed description, therefore, is not to betaken in a limiting sense, and the scope of the present disclosure isdefined by the appended claims.

For instance, it is understood that a disclosure in connection with adescribed method may also hold true for a corresponding device or systemconfigured to perform the method and vice versa. For example, if one ora plurality of method steps are described, a corresponding device mayinclude one or a plurality of units, e.g. functional units, to performthe described one or plurality of method steps (e.g. one unit performingthe one or plurality of steps, or a plurality of units each performingone or more of the plurality of steps), even if such one or more unitsare not explicitly described or illustrated in the figures. On the otherhand, for example, if an apparatus is described based on one or aplurality of units, e.g. functional units, a corresponding method mayinclude one step to perform the functionality of the one or plurality ofunits (e.g. one step performing the functionality of the one orplurality of units, or a plurality of steps each performing thefunctionality of one or more of the plurality of units), even if suchone or plurality of steps are not explicitly described or illustrated inthe figures. Further, it is understood that the features of the variousexemplary embodiments and/or aspects described herein may be combinedwith each other, unless noted otherwise.

Video coding typically refers to the processing of a sequence ofpictures, which form the video or video sequence. Instead of the term“picture” the term “frame” or “image” may be used as synonyms in thefield of video coding. Video coding (or coding in general) comprises twoparts video encoding and video decoding. Video encoding is performed atthe source side, typically comprising processing (e.g. by compression)the original video pictures to reduce the amount of data required forrepresenting the video pictures (for more efficient storage and/ortransmission). Video decoding is performed at the destination side andtypically comprises the inverse processing compared to the encoder toreconstruct the video pictures. Embodiments referring to “coding” ofvideo pictures (or pictures in general) shall be understood to relate to“encoding” or “decoding” of video pictures or respective videosequences. The combination of the encoding part and the decoding part isalso referred to as coding and decoding (CODEC).

In case of lossless video coding, the original video pictures can bereconstructed, i.e. the reconstructed video pictures have the samequality as the original video pictures (assuming no transmission loss orother data loss during storage or transmission). In case of lossy videocoding, further compression, e.g. by quantization, is performed, toreduce the amount of data representing the video pictures, which cannotbe completely reconstructed at the decoder, i.e. the quality of thereconstructed video pictures is lower or worse compared to the qualityof the original video pictures.

Several video coding standards belong to the group of “lossy hybridvideo codecs” (i.e. combine spatial and temporal prediction in thesample domain and two-dimensional (2D) transform coding for applyingquantization in the transform domain). Each picture of a video sequenceis typically partitioned into a set of non-overlapping blocks and thecoding is typically performed on a block level. In other words, at theencoder the video is typically processed, i.e. encoded, on a block(video block) level, e.g. using spatial (intra picture) predictionand/or temporal (inter picture) prediction to generate a predictionblock, subtracting the prediction block from the current block (blockcurrently processed/to be processed) to obtain a residual block,transforming the residual block and quantizing the residual block in thetransform domain to reduce the amount of data to be transmitted(compression), whereas at the decoder the inverse processing compared tothe encoder is applied to the encoded or compressed block to reconstructthe current block for representation. Furthermore, the encoderduplicates the decoder processing loop such that both will generateidentical predictions (e.g. intra- and inter predictions) and/orre-constructions for processing, i.e. coding, the subsequent blocks.

In the following embodiments of a video coding system 10, a videoencoder 20 and a video decoder 30 are described based on FIGS. 1 to 3.

FIG. 1A is a schematic block diagram illustrating an example codingsystem 10, e.g. a video coding system 10 (or short coding system 10)that may utilize techniques of this present application. Video encoder20 (or short encoder 20) and video decoder 30 (or short decoder 30) ofvideo coding system 10 represent examples of devices that may beconfigured to perform techniques in accordance with various examplesdescribed in the present application.

As shown in FIG. 1A, the coding system 10 comprises a source device 12configured to provide encoded picture data 21 e.g. to a destinationdevice 14 for decoding the encoded picture data 13.

The source device 12 comprises an encoder 20, and may additionally, i.e.optionally, comprise a picture source 16, a pre-processor (orpre-processing unit) 18, e.g. a picture pre-processor 18, and acommunication interface or communication unit 22.

The picture source 16 may comprise or be any kind of picture capturingdevice, for example a camera for capturing a real-world picture, and/orany kind of a picture generating device, for example a computer-graphicsprocessor for generating a computer animated picture, or any kind ofother device for obtaining and/or providing a real-world picture, acomputer generated picture (e.g. a screen content, a virtual reality(VR) picture) and/or any combination thereof (e.g. an augmented reality(AR) picture). The picture source may be any kind of memory or storagestoring any of the aforementioned pictures.

In distinction to the pre-processor 18 and the processing performed bythe pre-processing unit 18, the picture or picture data 17 may also bereferred to as raw picture or raw picture data 17.

Pre-processor 18 is configured to receive the (raw) picture data 17 andto perform pre-processing on the picture data 17 to obtain apre-processed picture 19 or pre-processed picture data 19.Pre-processing performed by the pre-processor 18 may, e.g., comprisetrimming, color format conversion (e.g. from RGB to YCbCr), colorcorrection, or de-noising. It can be understood that the pre-processingunit 18 may be optional component.

The video encoder 20 is configured to receive the pre-processed picturedata 19 and provide encoded picture data 21 (further details will bedescribed below, e.g., based on FIG. 2).

Communication interface 22 of the source device 12 may be configured toreceive the encoded picture data 21 and to transmit the encoded picturedata 21 (or any further processed version thereof) over communicationchannel 13 to another device, e.g. the destination device 14 or anyother device, for storage or direct reconstruction.

The destination device 14 comprises a decoder 30 (e.g. a video decoder30), and may additionally, i.e. optionally, comprise a communicationinterface or communication unit 28, a post-processor 32 (orpost-processing unit 32) and a display device 34.

The communication interface 28 of the destination device 14 isconfigured receive the encoded picture data 21 (or any further processedversion thereof), e.g. directly from the source device 12 or from anyother source, e.g. a storage device, e.g. an encoded picture datastorage device, and provide the encoded picture data 21 to the decoder30.

The communication interface 22 and the communication interface 28 may beconfigured to transmit or receive the encoded picture data 21 or encodeddata 13 via a direct communication link between the source device 12 andthe destination device 14, e.g. a direct wired or wireless connection,or via any kind of network, e.g. a wired or wireless network or anycombination thereof, or any kind of private and public network, or anykind of combination thereof.

The communication interface 22 may be configured to package the encodedpicture data 21 into an appropriate format, e.g. packets, and/or processthe encoded picture data using any kind of transmission encoding orprocessing for transmission over a communication link or communicationnetwork.

The communication interface 28, forming the counterpart of thecommunication interface 22, may be configured to receive the transmitteddata and process the transmission data using any kind of correspondingtransmission decoding or processing and/or de-packaging to obtain theencoded picture data 21.

Both, communication interface 22 and communication interface 28 may beconfigured as unidirectional communication interfaces as indicated bythe arrow for the communication channel 13 in FIG. 1A pointing from thesource device 12 to the destination device 14, or bi-directionalcommunication interfaces, and may be configured, e.g. to send andreceive messages, e.g. to set up a connection, to acknowledge andexchange any other information related to the communication link and/ordata transmission, e.g. encoded picture data transmission.

The decoder 30 is configured to receive the encoded picture data 21 andprovide decoded picture data 31 or a decoded picture 31 (further detailswill be described below, e.g., based on FIG. 3 or FIG. 5).

The post-processor 32 of destination device 14 is configured topost-process the decoded picture data 31 (also called reconstructedpicture data), e.g. the decoded picture 31, to obtain post-processedpicture data 33, e.g. a post-processed picture 33. The post-processingperformed by the post-processing unit 32 may comprise, e.g. color formatconversion (e.g. from YCbCr to RGB), color correction, trimming, orre-sampling, or any other processing, e.g. for preparing the decodedpicture data 31 for display, e.g. by display device 34.

The display device 34 of the destination device 14 is configured toreceive the post-processed picture data 33 for displaying the picture,e.g. to a user or viewer. The display device 34 may be or comprise anykind of display for representing the reconstructed picture, e.g. anintegrated or external display or monitor. The displays may, e.g.comprise liquid crystal displays (LCD), organic light emitting diodes(OLED) displays, plasma displays, projectors, micro light emitting diode(LED) displays, liquid crystal on silicon (LcoS), digital lightprocessor (DLP) or any kind of other display.

Although FIG. 1A depicts the source device 12 and the destination device14 as separate devices, embodiments of devices may also comprise both orboth functionalities, the source device 12 or correspondingfunctionality and the destination device 14 or correspondingfunctionality. In such embodiments the source device 12 or correspondingfunctionality and the destination device 14 or correspondingfunctionality may be implemented using the same hardware and/or softwareor by separate hardware and/or software or any combination thereof.

As will be apparent for the skilled person based on the description, theexistence and (exact) split of functionalities of the different units orfunctionalities within the source device 12 and/or destination device 14as shown in FIG. 1A may vary depending on the device and application.

The encoder 20 (e.g. a video encoder 20) or the decoder 30 (e.g. a videodecoder 30) or both encoder 20 and decoder 30 may be implemented viaprocessing circuitry as shown in FIG. 1B, such as one or moremicroprocessors, digital signal processors (DSPs), application-specificintegrated circuits (ASICs), field-programmable gate arrays (FPGAs),discrete logic, hardware, video coding dedicated or any combinationsthereof. The encoder 20 may be implemented via processing circuitry 46to embody the various modules as discussed with respect to encoder 20 ofFIG. 2 and/or any other encoder system or subsystem described herein.The decoder 30 may be implemented via processing circuitry 46 to embodythe various modules as discussed with respect to decoder 30 of FIG. 3and/or any other decoder system or subsystem described herein. Theprocessing circuitry may be configured to perform the various operationsas discussed later. As shown in FIG. 5, if the techniques areimplemented partially in software, a device may store instructions forthe software in a suitable, non-transitory computer-readable storagemedium and may execute the instructions in hardware using one or moreprocessors to perform the techniques of this disclosure. Either of videoencoder 20 and video decoder 30 may be integrated as part of a combinedencoder/decoder (CODEC) in a single device, for example, as shown inFIG. 1B.

Source device 12 and destination device 14 may comprise any of a widerange of devices, including any kind of handheld or stationary devices,e.g. notebook or laptop computers, mobile phones, smart phones, tabletsor tablet computers, cameras, desktop computers, set-top boxes,televisions, display devices, digital media players, video gamingconsoles, video streaming devices (such as content services servers orcontent delivery servers), broadcast receiver device, broadcasttransmitter device, or the like and may use no or any kind of operatingsystem. In some cases, the source device 12 and the destination device14 may be equipped for wireless communication. Thus, the source device12 and the destination device 14 may be wireless communication devices.

In some cases, video coding system 10 illustrated in FIG. 1A is merelyan example and the techniques of the present application may apply tovideo coding settings (e.g., video encoding or video decoding) that donot necessarily include any data communication between the encoding anddecoding devices. In other examples, data is retrieved from a localmemory, streamed over a network, or the like. A video encoding devicemay encode and store data to memory, and/or a video decoding device mayretrieve and decode data from memory. In some examples, the encoding anddecoding is performed by devices that do not communicate with oneanother, but simply encode data to memory and/or retrieve and decodedata from memory.

For convenience of description, embodiments of the present disclosureare described herein, for example, by reference to High-Efficiency VideoCoding (HEVC) or to the reference software of Versatile Video coding(VVC), the next generation video coding standard developed by the JointCollaboration Team on Video Coding (JCT-VC) of ITU-T Video CodingExperts Group (VCEG) and ISO/IEC Motion Picture Experts Group (MPEG).One of ordinary skill in the art will understand that embodiments of thepresent disclosure are not limited to HEVC or VVC.

Encoder and Encoding Method

FIG. 2 shows a schematic block diagram of an example video encoder 20that is configured to implement the techniques of the presentapplication. In the example of FIG. 2, the video encoder 20 comprises aninput 201 (or input interface 201), a residual calculation unit 204, atransform processing unit 206, a quantization unit 208, an inversequantization unit 210, and inverse transform processing unit 212, areconstruction unit 214, a loop filter unit 220, a decoded picturebuffer (DPB) 230, a mode selection unit 260, an entropy encoding unit270 and an output 272 (or output interface 272). The mode selection unit260 may include an inter prediction unit 244, an intra prediction unit254 and a partitioning unit 262. Inter prediction unit 244 may include amotion estimation unit and a motion compensation unit (not shown). Avideo encoder 20 as shown in FIG. 2 may also be referred to as hybridvideo encoder or a video encoder based on a hybrid video codec.

The residual calculation unit 204, the transform processing unit 206,the quantization unit 208, the mode selection unit 260 may be referredto as forming a forward signal path of the encoder 20, whereas theinverse quantization unit 210, the inverse transform processing unit212, the reconstruction unit 214, the buffer 216, the loop filter 220,the decoded picture buffer (DPB) 230, the inter prediction unit 244 andthe intra-prediction unit 254 may be referred to as forming a backwardsignal path of the video encoder 20, wherein the backward signal path ofthe video encoder 20 corresponds to the signal path of the decoder (seevideo decoder 30 in FIG. 3). The inverse quantization unit 210, theinverse transform processing unit 212, the reconstruction unit 214, theloop filter 220, the decoded picture buffer (DPB) 230, the interprediction unit 244 and the intra-prediction unit 254 are also referredto forming the “built-in decoder” of video encoder 20.

Pictures & Picture Partitioning (Pictures & Blocks)

The encoder 20 may be configured to receive, e.g. via input 201, apicture 17 (or picture data 17), e.g. picture of a sequence of picturesforming a video or video sequence. The received picture or picture datamay also be a pre-processed picture 19 (or pre-processed picture data19). For sake of simplicity, the following description refers to thepicture 17. The picture 17 may also be referred to as current picture orpicture to be coded (in particular in video coding to distinguish thecurrent picture from other pictures, e.g. previously encoded and/ordecoded pictures of the same video sequence, i.e. the video sequencewhich also comprises the current picture).

A (digital) picture is or can be regarded as a two-dimensional array ormatrix of samples with intensity values. A sample in the array may alsobe referred to as pixel (short form of picture element) or a pel. Thenumber of samples in horizontal and vertical direction (or axis) of thearray or picture define the size and/or resolution of the picture. Forrepresentation of color, typically three color components are employed,i.e. the picture may be represented or include three sample arrays. InRBG format or color space a picture comprises a corresponding red, greenand blue sample array. However, in video coding each pixel is typicallyrepresented in a luminance and chrominance format or color space, e.g.YcbCr, which comprises a luminance component indicated by Y (sometimesalso L is used instead) and two chrominance components indicated by Cband Cr. The luminance (or short luma) component Y represents thebrightness or grey level intensity (e.g. like in a grey-scale picture),while the two chrominance (or short chroma) components Cb and Crrepresent the chromaticity or color information components. Accordingly,a picture in YcbCr format comprises a luminance sample array ofluminance sample values (Y), and two chrominance sample arrays ofchrominance values (Cb and Cr). Pictures in RGB format may be convertedor transformed into YcbCr format and vice versa, the process is alsoknown as color transformation or conversion. If a picture is monochrome,the picture may comprise only a luminance sample array. Accordingly, apicture may be, for example, an array of luma samples in monochromeformat or an array of luma samples and two corresponding arrays ofchroma samples in 4:2:0, 4:2:2, and 4:4:4 colour format.

Embodiments of the video encoder 20 may comprise a picture partitioningunit (not depicted in FIG. 2) configured to partition the picture 17into a plurality of (typically non-overlapping) picture blocks 203.These blocks may also be referred to as root blocks, macro blocks(H.264/AVC) or coding tree blocks (CTB) or coding tree units (CTU)(H.265/HEVC and VVC). The picture partitioning unit may be configured touse the same block size for all pictures of a video sequence and thecorresponding grid defining the block size, or to change the block sizebetween pictures or subsets or groups of pictures, and partition eachpicture into the corresponding blocks.

In further embodiments, the video encoder may be configured to receivedirectly a block 203 of the picture 17, e.g. one, several or all blocksforming the picture 17. The picture block 203 may also be referred to ascurrent picture block or picture block to be coded.

Like the picture 17, the picture block 203 again is or can be regardedas a two-dimensional array or matrix of samples with intensity values(sample values), although of smaller dimension than the picture 17. Inother words, the block 203 may comprise, e.g., one sample array (e.g. aluma array in case of a monochrome picture 17, or a luma or chroma arrayin case of a color picture) or three sample arrays (e.g. a luma and twochroma arrays in case of a color picture 17) or any other number and/orkind of arrays depending on the color format applied. The number ofsamples in horizontal and vertical direction (or axis) of the block 203define the size of block 203. Accordingly, a block may, for example, anM×N (M-column by N-row) array of samples, or an M×N array of transformcoefficients.

Embodiments of the video encoder 20 as shown in FIG. 2 may be configuredto encode the picture 17 block by block, e.g. the encoding andprediction is performed per block 203.

Embodiments of the video encoder 20 as shown in FIG. 2 may be furtherconfigured to partition and/or encode the picture using slices (alsoreferred to as video slices), wherein a picture may be partitioned intoor encoded using one or more slices (typically non-overlapping), andeach slice may comprise one or more blocks (e.g. CTUs).

Embodiments of the video encoder 20 as shown in FIG. 2 may be furtherconfigured to partition and/or encode the picture using tile groups(also referred to as video tile groups) and/or tiles (also referred toas video tiles), wherein a picture may be partitioned into or encodedusing one or more tile groups (typically non-overlapping), and each tilegroup may comprise, e.g. one or more blocks (e.g. CTUs) or one or moretiles, wherein each tile, e.g. may be of rectangular shape and maycomprise one or more blocks (e.g. CTUs), e.g. complete or fractionalblocks.

Residual Calculation

The residual calculation unit 204 may be configured to calculate aresidual block 205 (also referred to as residual 205) based on thepicture block 203 and a prediction block 265 (further details about theprediction block 265 are provided later), e.g. by subtracting samplevalues of the prediction block 265 from sample values of the pictureblock 203, sample by sample (pixel by pixel) to obtain the residualblock 205 in the sample domain.

Transform

The transform processing unit 206 may be configured to apply atransform, e.g. a discrete cosine transform (DCT) or discrete sinetransform (DST), on the sample values of the residual block 205 toobtain transform coefficients 207 in a transform domain. The transformcoefficients 207 may also be referred to as transform residualcoefficients and represent the residual block 205 in the transformdomain.

The transform processing unit 206 may be configured to apply integerapproximations of DCT/DST, such as the transforms specified forH.265/HEVC. Compared to an orthogonal DCT transform, such integerapproximations are typically scaled by a certain factor. In order topreserve the norm of the residual block which is processed by forwardand inverse transforms, additional scaling factors are applied as partof the transform process. The scaling factors are typically chosen basedon certain constraints like scaling factors being a power of two forshift operations, bit depth of the transform coefficients, tradeoffbetween accuracy and implementation costs, etc. Specific scaling factorsare, for example, specified for the inverse transform, e.g. by inversetransform processing unit 212 (and the corresponding inverse transform,e.g. by inverse transform processing unit 312 at video decoder 30) andcorresponding scaling factors for the forward transform, e.g. bytransform processing unit 206, at an encoder 20 may be specifiedaccordingly.

Embodiments of the video encoder 20 (respectively transform processingunit 206) may be configured to output transform parameters, e.g. a typeof transform or transforms, e.g. directly or encoded or compressed viathe entropy encoding unit 270, such that, e.g., the video decoder 30 mayreceive and use the transform parameters for decoding.

Quantization

The quantization unit 208 may be configured to quantize the transformcoefficients 207 to obtain quantized coefficients 209, e.g. by applyingscalar quantization or vector quantization. The quantized coefficients209 may also be referred to as quantized transform coefficients 209 orquantized residual coefficients 209.

The quantization process may reduce the bit depth associated with someor all of the transform coefficients 207. For example, an n-bittransform coefficient may be rounded down to an m-bit Transformcoefficient during quantization, where n is greater than m. The degreeof quantization may be modified by adjusting a quantization parameter(QP). For example for scalar quantization, different scaling may beapplied to achieve finer or coarser quantization. Smaller quantizationstep sizes correspond to finer quantization, whereas larger quantizationstep sizes correspond to coarser quantization. The applicablequantization step size may be indicated by a quantization parameter(QP). The quantization parameter may for example be an index to apredefined set of applicable quantization step sizes. For example, smallquantization parameters may correspond to fine quantization (smallquantization step sizes) and large quantization parameters maycorrespond to coarse quantization (large quantization step sizes) orvice versa. The quantization may include division by a quantization stepsize and a corresponding and/or the inverse dequantization, e.g. byinverse quantization unit 210, may include multiplication by thequantization step size. Embodiments based on some standards, e.g. HEVC,may be configured to use a quantization parameter to determine thequantization step size. Generally, the quantization step size may becalculated based on a quantization parameter using a fixed pointapproximation of an equation including division. Additional scalingfactors may be introduced for quantization and dequantization to restorethe norm of the residual block, which might get modified because of thescaling used in the fixed point approximation of the equation forquantization step size and quantization parameter. In one exampleimplementation, the scaling of the inverse transform and dequantizationmight be combined. In an example, customized quantization tables may beused and signaled from an encoder to a decoder, e.g. in a bitstream. Thequantization is a lossy operation, wherein the loss increases withincreasing quantization step sizes.

Embodiments of the video encoder 20 (respectively quantization unit 208)may be configured to output quantization parameters (QP), e.g. directlyor encoded via the entropy encoding unit 270, such that, e.g., the videodecoder 30 may receive and apply the quantization parameters fordecoding.

Inverse Quantization

The inverse quantization unit 210 is configured to apply the inversequantization of the quantization unit 208 on the quantized coefficientsto obtain dequantized coefficients 211, e.g. by applying the inverse ofthe quantization scheme applied by the quantization unit 208 based on orusing the same quantization step size as the quantization unit 208. Thedequantized coefficients 211 may also be referred to as dequantizedresidual coefficients 211 and correspond—although typically notidentical to the transform coefficients due to the loss byquantization—to the transform coefficients 207.

Inverse Transform

The inverse transform processing unit 212 is configured to apply theinverse transform of the transform applied by the transform processingunit 206, e.g. an inverse discrete cosine transform (DCT) or inversediscrete sine transform (DST) or other inverse transforms, to obtain areconstructed residual block 213 (or corresponding dequantizedcoefficients 213) in the sample domain. The reconstructed residual block213 may also be referred to as transform block 213.

Reconstruction

The reconstruction unit 214 (e.g. adder or summer 214) is configured toadd the transform block 213 (i.e. reconstructed residual block 213) tothe prediction block 265 to obtain a reconstructed block 215 in thesample domain, e.g. by adding—sample by sample—the sample values of thereconstructed residual block 213 and the sample values of the predictionblock 265.

Filtering

The loop filter unit 220 (or short “loop filter” 220), is configured tofilter the reconstructed block 215 to obtain a filtered block 221, or ingeneral, to filter reconstructed samples to obtain filtered samples. Theloop filter unit is, e.g., configured to smooth pixel transitions, orotherwise improve the video quality. The loop filter unit 220 maycomprise one or more loop filters such as a de-blocking filter, asample-adaptive offset (SAO) filter or one or more other filters, e.g. abilateral filter, an adaptive loop filter (ALF), a sharpening, asmoothing filters or a collaborative filters, or any combinationthereof. Although the loop filter unit 220 is shown in FIG. 2 as beingan in loop filter, in other configurations, the loop filter unit 220 maybe implemented as a post loop filter. The filtered block 221 may also bereferred to as filtered reconstructed block 221.

Embodiments of the video encoder 20 (respectively loop filter unit 220)may be configured to output loop filter parameters (such as sampleadaptive offset information), e.g. directly or encoded via the entropyencoding unit 270, such that, e.g., a decoder 30 may receive and applythe same loop filter parameters or respective loop filters for decoding.

Decoded Picture Buffer

The decoded picture buffer (DPB) 230 may be a memory that storesreference pictures, or in general reference picture data, for encodingvideo data by video encoder 20. The DPB 230 may be formed by any of avariety of memory devices, such as dynamic random access memory (DRAM),including synchronous DRAM (SDRAM), magnetoresistive random accessmemory (MRAM), resistive random access memory (RRAM), or other types ofmemory devices. The decoded picture buffer (DPB) 230 may be configuredto store one or more filtered blocks 221. The decoded picture buffer 230may be further configured to store other previously filtered blocks,e.g. previously reconstructed and filtered blocks 221, of the samecurrent picture or of different pictures, e.g. previously reconstructedpictures, and may provide complete previously reconstructed, i.e.decoded, pictures (and corresponding reference blocks and samples)and/or a partially reconstructed current picture (and correspondingreference blocks and samples), for example for inter prediction. Thedecoded picture buffer (DPB) 230 may be also configured to store one ormore unfiltered reconstructed blocks 215, or in general unfilteredreconstructed samples, e.g. if the reconstructed block 215 is notfiltered by loop filter unit 220, or any other further processed versionof the reconstructed blocks or samples.

Mode Selection (Partitioning & Prediction)

The mode selection unit 260 comprises partitioning unit 262,inter-prediction unit 244 and intra-prediction unit 254, and isconfigured to receive or obtain original picture data, e.g. an originalblock 203 (current block 203 of the current picture 17), andreconstructed picture data, e.g. filtered and/or unfilteredreconstructed samples or blocks of the same (current) picture and/orfrom one or a plurality of previously decoded pictures, e.g. fromdecoded picture buffer 230 or other buffers (e.g. line buffer, notshown). The reconstructed picture data is used as reference picture datafor prediction, e.g. inter-prediction or intra-prediction, to obtain aprediction block 265 or predictor 265.

Mode selection unit 260 may be configured to determine or select apartitioning for a current block prediction mode (including nopartitioning) and a prediction mode (e.g. an intra or inter predictionmode) and generate a corresponding prediction block 265, which is usedfor the calculation of the residual block 205 and for the reconstructionof the reconstructed block 215.

Embodiments of the mode selection unit 260 may be configured to selectthe partitioning and the prediction mode (e.g. from those supported byor available for mode selection unit 260), which provide the best matchor in other words the minimum residual (minimum residual means bettercompression for transmission or storage), or a minimum signalingoverhead (minimum signaling overhead means better compression fortransmission or storage), or which considers or balances both. The modeselection unit 260 may be configured to determine the partitioning andprediction mode based on rate distortion optimization (RDO), i.e. selectthe prediction mode, which provides a minimum rate distortion. Termslike “best”, “minimum”, “optimum” etc. in this context do notnecessarily refer to an overall “best”, “minimum”, “optimum”, etc. butmay also refer to the fulfillment of a termination or selectioncriterion like a value exceeding or falling below a threshold or otherconstraints leading potentially to a “sub-optimum selection” butreducing complexity and processing time.

In other words, the partitioning unit 262 may be configured to partitionthe block 203 into smaller block partitions or sub-blocks (which formagain blocks), e.g. iteratively using quad-tree-partitioning (QT),binary partitioning (BT) or triple-tree-partitioning (TT) or anycombination thereof, and to perform, e.g., the prediction for each ofthe block partitions or sub-blocks, wherein the mode selection comprisesthe selection of the tree-structure of the partitioned block 203 and theprediction modes are applied to each of the block partitions orsub-blocks.

In the following the partitioning (e.g. by partitioning unit 260) andprediction processing (by inter-prediction unit 244 and intra-predictionunit 254) performed by an example video encoder 20 will be explained inmore detail.

Partitioning

The partitioning unit 262 may partition (or split) a current block 203into smaller partitions, e.g. smaller blocks of square or rectangularsize. These smaller blocks (which may also be referred to as sub-blocks)may be further partitioned into even smaller partitions. This is alsoreferred to tree-partitioning or hierarchical tree-partitioning, whereina root block, e.g. at root tree-level 0 (hierarchy-level 0, depth 0),may be recursively partitioned, e.g. partitioned into two or more blocksof a next lower tree-level, e.g. nodes at tree-level 1 (hierarchy-level1, depth 1), wherein these blocks may be again partitioned into two ormore blocks of a next lower level, e.g. tree-level 2 (hierarchy-level 2,depth 2), etc. until the partitioning is terminated, e.g. because atermination criterion is fulfilled, e.g. a maximum tree depth or minimumblock size is reached. Blocks, which are not further partitioned, arealso referred to as leaf-blocks or leaf nodes of the tree. A tree usingpartitioning into two partitions is referred to as binary-tree (BT), atree using partitioning into three partitions is referred to asternary-tree (TT), and a tree using partitioning into four partitions isreferred to as quad-tree (QT).

As mentioned before, the term “block” as used herein may be a portion,in particular a square or rectangular portion, of a picture. Withreference, for example, to HEVC and VVC, the block may be or correspondto a coding tree unit (CTU), a coding unit (CU), prediction unit (PU),and transform unit (TU) and/or to the corresponding blocks, e.g. acoding tree block (CTB), a coding block (CB), a transform block (TB) orprediction block (PB).

For example, a coding tree unit (CTU) may be or comprise a CTB of lumasamples, two corresponding CTBs of chroma samples of a picture that hasthree sample arrays, or a CTB of samples of a monochrome picture or apicture that is coded using three separate colour planes and syntaxstructures used to code the samples. Correspondingly, a coding treeblock (CTB) may be an N×N block of samples for some value of N such thatthe division of a component into CTBs is a partitioning. A coding unit(CU) may be or comprise a coding block of luma samples, twocorresponding coding blocks of chroma samples of a picture that hasthree sample arrays, or a coding block of samples of a monochromepicture or a picture that is coded using three separate colour planesand syntax structures used to code the samples. Correspondingly, acoding block (CB) may be an M×N block of samples for some values of Mand N such that the division of a CTB into coding blocks is apartitioning.

In embodiments, e.g., based on HEVC, a coding tree unit (CTU) may besplit into Cus using a quad-tree structure denoted as coding tree. Thedecision whether to code a picture area using inter-picture (temporal)or intra-picture (spatial) prediction is made at the CU level. Each CUcan be further split into one, two or four Pus based on the PU splittingtype. Inside one PU, the same prediction process is applied and therelevant information is transmitted to the decoder on a PU basis. Afterobtaining the residual block by applying the prediction process based onthe PU splitting type, a CU can be partitioned into transform units(Tus) based on another quadtree structure similar to the coding tree forthe CU.

In embodiments, e.g., based on the latest video coding standardcurrently in development, which is referred to as Versatile Video Coding(VVC), a combined Quad-tree and binary tree (QTBT) partitioning is forexample used to partition a coding block. In the QTBT block structure, aCU can have either a square or a rectangular shape. For example, acoding tree unit (CTU) is first partitioned by a quadtree structure. Thequadtree leaf nodes are further partitioned by a binary tree or ternary(or triple) tree structure. The partitioning tree leaf nodes are calledcoding units (Cus), and that segmentation is used for prediction andtransform processing without any further partitioning. This means thatthe CU, PU and TU have the same block size in the QTBT coding blockstructure. In parallel, multiple partition, for example, triple treepartition may be used together with the QTBT block structure.

In one example, the mode selection unit 260 of video encoder 20 may beconfigured to perform any combination of the partitioning techniquesdescribed herein.

As described above, the video encoder 20 is configured to determine orselect the best or an optimum prediction mode from a set of (e.g.pre-determined) prediction modes. The set of prediction modes maycomprise, e.g., intra-prediction modes and/or inter-prediction modes.

Intra-Prediction

The set of intra-prediction modes may comprise 35 differentintra-prediction modes, e.g. non-directional modes like DC (or mean)mode and planar mode, or directional modes, e.g. as defined in HEVC, ormay comprise 67 different intra-prediction modes, e.g. non-directionalmodes like DC (or mean) mode and planar mode, or directional modes, e.g.as defined for VVC.

The intra-prediction unit 254 is configured to use reconstructed samplesof neighboring blocks of the same current picture to generate anintra-prediction block 265 based on an intra-prediction mode of the setof intra-prediction modes.

The intra prediction unit 254 (or in general the mode selection unit260) is further configured to output intra-prediction parameters (or ingeneral information indicative of the selected intra prediction mode forthe block) to the entropy encoding unit 270 in form of syntax elements266 for inclusion into the encoded picture data 21 such that, e.g., thevideo decoder 30 may receive and use the prediction parameters fordecoding.

Inter-Prediction

The set of (or possible) inter-prediction modes depends on the availablereference pictures (i.e. previous at least partially decoded pictures,e.g. stored in DBP 230) and other inter-prediction parameters, e.g.whether the whole reference picture or only a part, e.g. a search windowarea around the area of the current block, of the reference picture isused for searching for a best matching reference block, and/or e.g.whether pixel interpolation is applied, e.g. half/semi-pel and/orquarter-pel interpolation, or not.

Additional to the above prediction modes, skip mode and/or direct modemay be applied.

The inter prediction unit 244 may include a motion estimation (ME) unitand a motion compensation (MC) unit (both not shown in FIG. 2). Themotion estimation unit may be configured to receive or obtain thepicture block 203 (current picture block 203 of the current picture 17)and a decoded picture 231, or at least one or a plurality of previouslyreconstructed blocks, e.g. reconstructed blocks of one or a plurality ofother/different previously decoded pictures 231, for motion estimation.E.g. a video sequence may comprise the current picture and thepreviously decoded pictures 231, or in other words, the current pictureand the previously decoded pictures 231 may be part of or form asequence of pictures forming a video sequence.

The encoder 20 may, e.g., be configured to select a reference block froma plurality of reference blocks of the same or different pictures of theplurality of other pictures and provide a reference picture (orreference picture index) and/or an offset (spatial offset) between theposition (x, y coordinates) of the reference block and the position ofthe current block as inter prediction parameters to the motionestimation unit. This offset is also called motion vector (MV).

The motion compensation unit is configured to obtain, e.g. receive, aninter prediction parameter and to perform inter prediction based on orusing the inter prediction parameter to obtain an inter prediction block265. Motion compensation, performed by the motion compensation unit, mayinvolve fetching or generating the prediction block based on themotion/block vector determined by motion estimation, possibly performinginterpolations to sub-pixel precision. Interpolation filtering maygenerate additional pixel samples from known pixel samples, thuspotentially increasing the number of candidate prediction blocks thatmay be used to code a picture block. Upon receiving the motion vectorfor the PU of the current picture block, the motion compensation unitmay locate the prediction block to which the motion vector points in oneof the reference picture lists.

The motion compensation unit may also generate syntax elementsassociated with the blocks and video slices for use by video decoder 30in decoding the picture blocks of the video slice. In addition or as analternative to slices and respective syntax elements, tile groups and/ortiles and respective syntax elements may be generated or used.

Entropy Coding

The entropy encoding unit 270 is configured to apply, for example, anentropy encoding algorithm or scheme (e.g. a variable length coding(VLC) scheme, an context adaptive VLC scheme (CAVLC), an arithmeticcoding scheme, a binarization, a context adaptive binary arithmeticcoding (CABAC), syntax-based context-adaptive binary arithmetic coding(SBAC), probability interval partitioning entropy (PIPE) coding oranother entropy encoding methodology or technique) or bypass (nocompression) on the quantized coefficients 209, inter predictionparameters, intra prediction parameters, loop filter parameters and/orother syntax elements to obtain encoded picture data 21 which can beoutput via the output 272, e.g. in the form of an encoded bitstream 21such that, e.g., the video decoder 30 may receive and use the parametersfor decoding. The encoded bitstream 21 may be transmitted to videodecoder 30, or stored in a memory for later transmission or retrieval byvideo decoder 30.

Other structural variations of the video encoder 20 can be used toencode the video stream. For example, a non-transform based encoder 20can quantize the residual signal directly without the transformprocessing unit 206 for certain blocks or frames. In anotherimplementation, an encoder 20 can have the quantization unit 208 and theinverse quantization unit 210 combined into a single unit.

Decoder and Decoding Method

FIG. 3 shows an example of a video decoder 30 that is configured toimplement the techniques of this present application. The video decoder30 is configured to receive encoded picture data 21 (e.g. encodedbitstream 21), e.g. encoded by encoder 20, to obtain a decoded picture331. The encoded picture data or bitstream comprises information fordecoding the encoded picture data, e.g. data that represents pictureblocks of an encoded video slice (and/or tile groups or tiles) andassociated syntax elements.

In the example of FIG. 3, the decoder 30 comprises an entropy decodingunit 304, an inverse quantization unit 310, an inverse transformprocessing unit 312, a reconstruction unit 314 (e.g. a summer 314), aloop filter 320, a decoded picture buffer (DBP) 330, a mode applicationunit 360, an inter prediction unit 344 and an intra prediction unit 354.Inter prediction unit 344 may be or include a motion compensation unit.Video decoder 30 may, in some examples, perform a decoding passgenerally reciprocal to the encoding pass described with respect tovideo encoder 100 from FIG. 2.

As explained with regard to the encoder 20, the inverse quantizationunit 210, the inverse transform processing unit 212, the reconstructionunit 214 the loop filter 220, the decoded picture buffer (DPB) 230, theinter prediction unit 344 and the intra prediction unit 354 are alsoreferred to as forming the “built-in decoder” of video encoder 20.Accordingly, the inverse quantization unit 310 may be identical infunction to the inverse quantization unit 110, the inverse transformprocessing unit 312 may be identical in function to the inversetransform processing unit 212, the reconstruction unit 314 may beidentical in function to reconstruction unit 214, the loop filter 320may be identical in function to the loop filter 220, and the decodedpicture buffer 330 may be identical in function to the decoded picturebuffer 230. Therefore, the explanations provided for the respectiveunits and functions of the video 20 encoder apply correspondingly to therespective units and functions of the video decoder 30.

Entropy Decoding

The entropy decoding unit 304 is configured to parse the bitstream 21(or in general encoded picture data 21) and perform, for example,entropy decoding to the encoded picture data 21 to obtain, e.g.,quantized coefficients 309 and/or decoded coding parameters (not shownin FIG. 3), e.g. any or all of inter prediction parameters (e.g.reference picture index and motion vector), intra prediction parameter(e.g. intra prediction mode or index), transform parameters,quantization parameters, loop filter parameters, and/or other syntaxelements. Entropy decoding unit 304 maybe configured to apply thedecoding algorithms or schemes corresponding to the encoding schemes asdescribed with regard to the entropy encoding unit 270 of the encoder20. Entropy decoding unit 304 may be further configured to provide interprediction parameters, intra prediction parameter and/or other syntaxelements to the mode application unit 360 and other parameters to otherunits of the decoder 30. Video decoder 30 may receive the syntaxelements at the video slice level and/or the video block level. Inaddition or as an alternative to slices and respective syntax elements,tile groups and/or tiles and respective syntax elements may be receivedand/or used.

Inverse Quantization

The inverse quantization unit 310 may be configured to receivequantization parameters (QP) (or in general information related to theinverse quantization) and quantized coefficients from the encodedpicture data 21 (e.g. by parsing and/or decoding, e.g. by entropydecoding unit 304) and to apply based on the quantization parameters aninverse quantization on the decoded quantized coefficients 309 to obtaindequantized coefficients 311, which may also be referred to as transformcoefficients 311. The inverse quantization process may include use of aquantization parameter determined by video encoder 20 for each videoblock in the video slice (or tile or tile group) to determine a degreeof quantization and, likewise, a degree of inverse quantization thatshould be applied.

Inverse Transform

Inverse transform processing unit 312 may be configured to receivedequantized coefficients 311, also referred to as transform coefficients311, and to apply a transform to the dequantized coefficients 311 inorder to obtain reconstructed residual blocks 213 in the sample domain.The reconstructed residual blocks 213 may also be referred to astransform blocks 313. The transform may be an inverse transform, e.g.,an inverse DCT, an inverse DST, an inverse integer transform, or aconceptually similar inverse transform process. The inverse transformprocessing unit 312 may be further configured to receive transformparameters or corresponding information from the encoded picture data 21(e.g. by parsing and/or decoding, e.g. by entropy decoding unit 304) todetermine the transform to be applied to the dequantized coefficients311.

Reconstruction

The reconstruction unit 314 (e.g. adder or summer 314) may be configuredto add the reconstructed residual block 313, to the prediction block 365to obtain a reconstructed block 315 in the sample domain, e.g. by addingthe sample values of the reconstructed residual block 313 and the samplevalues of the prediction block 365.

Filtering

The loop filter unit 320 (either in the coding loop or after the codingloop) is configured to filter the reconstructed block 315 to obtain afiltered block 321, e.g. to smooth pixel transitions, or otherwiseimprove the video quality. The loop filter unit 320 may comprise one ormore loop filters such as a de-blocking filter, a sample-adaptive offset(SAO) filter or one or more other filters, e.g. a bilateral filter, anadaptive loop filter (ALF), a sharpening, a smoothing filters or acollaborative filters, or any combination thereof. Although the loopfilter unit 320 is shown in FIG. 3 as being an in loop filter, in otherconfigurations, the loop filter unit 320 may be implemented as a postloop filter.

Decoded Picture Buffer

The decoded video blocks 321 of a picture are then stored in decodedpicture buffer 330, which stores the decoded pictures 331 as referencepictures for subsequent motion compensation for other pictures and/orfor output respectively display.

The decoder 30 is configured to output the decoded picture 311, e.g. viaoutput 312, for presentation or viewing to a user.

Prediction

The inter prediction unit 344 may be identical to the inter predictionunit 244 (in particular to the motion compensation unit) and the intraprediction unit 354 may be identical to the inter prediction unit 254 infunction, and performs split or partitioning decisions and predictionbased on the partitioning and/or prediction parameters or respectiveinformation received from the encoded picture data 21 (e.g. by parsingand/or decoding, e.g. by entropy decoding unit 304). Mode applicationunit 360 may be configured to perform the prediction (intra or interprediction) per block based on reconstructed pictures, blocks orrespective samples (filtered or unfiltered) to obtain the predictionblock 365.

When the video slice is coded as an intra coded (I) slice, intraprediction unit 354 of mode application unit 360 is configured togenerate prediction block 365 for a picture block of the current videoslice based on a signaled intra prediction mode and data from previouslydecoded blocks of the current picture. When the video picture is codedas an inter coded (i.e., B, or P) slice, inter prediction unit 344 (e.g.motion compensation unit) of mode application unit 360 is configured toproduce prediction blocks 365 for a video block of the current videoslice based on the motion vectors and other syntax elements receivedfrom entropy decoding unit 304. For inter prediction, the predictionblocks may be produced from one of the reference pictures within one ofthe reference picture lists. Video decoder 30 may construct thereference frame lists, List 0 and List 1, using default constructiontechniques based on reference pictures stored in DPB 330. The same orsimilar may be applied for or by embodiments using tile groups (e.g.video tile groups) and/or tiles (e.g. video tiles) in addition or in anexample, to slices (e.g. video slices), e.g. a video may be coded usingI, P or B tile groups and/or tiles.

Mode application unit 360 is configured to determine the predictioninformation for a video block of the current video slice by parsing themotion vectors or related information and other syntax elements, anduses the prediction information to produce the prediction blocks for thecurrent video block being decoded. For example, the mode applicationunit 360 uses some of the received syntax elements to determine aprediction mode (e.g., intra or inter prediction) used to code the videoblocks of the video slice, an inter prediction slice type (e.g., Bslice, P slice, or GPB slice), construction information for one or moreof the reference picture lists for the slice, motion vectors for eachinter encoded video block of the slice, inter prediction status for eachinter coded video block of the slice, and other information to decodethe video blocks in the current video slice. The same or similar may beapplied for or by embodiments using tile groups (e.g. video tile groups)and/or tiles (e.g. video tiles) in addition or in an example to slices(e.g. video slices), e.g. a video may be coded using I, P or B tilegroups and/or tiles.

Embodiments of the video decoder 30 as shown in FIG. 3 may be configuredto partition and/or decode the picture using slices (also referred to asvideo slices), wherein a picture may be partitioned into or decodedusing one or more slices (typically non-overlapping), and each slice maycomprise one or more blocks (e.g. CTUs).

Embodiments of the video decoder 30 as shown in FIG. 3 may be configuredto partition and/or decode the picture using tile groups (also referredto as video tile groups) and/or tiles (also referred to as video tiles),wherein a picture may be partitioned into or decoded using one or moretile groups (typically non-overlapping), and each tile group maycomprise, e.g. one or more blocks (e.g. CTUs) or one or more tiles,wherein each tile, e.g. may be of rectangular shape and may comprise oneor more blocks (e.g. CTUs), e.g. complete or fractional blocks.

Other variations of the video decoder 30 can be used to decode theencoded picture data 21. For example, the decoder 30 can produce theoutput video stream without the loop filtering unit 320. For example, anon-transform based decoder 30 can inverse-quantize the residual signaldirectly without the inverse-transform processing unit 312 for certainblocks or frames. In another implementation, the video decoder 30 canhave the inverse-quantization unit 310 and the inverse-transformprocessing unit 312 combined into a single unit.

It should be understood that, in the encoder 20 and the decoder 30, aprocessing result of a current step may be further processed and thenoutput to the next step. For example, after interpolation filtering,motion vector derivation or loop filtering, a further operation, such asClip or shift, may be performed on the processing result of theinterpolation filtering, motion vector derivation or loop filtering.

It should be noted that further operations may be applied to the derivedmotion vectors of current block (including but not limit to controlpoint motion vectors of affine mode, sub-block motion vectors in affine,planar, ATMVP modes, temporal motion vectors, and so on). For example,the value of motion vector is constrained to a predefined range based onits representing bit. If the representing bit of motion vector isbitDepth, then the range is −2{circumflex over( )}(bitDepth−1)˜2{circumflex over ( )}(bitDepth−1)−1, where“{circumflex over ( )}” means exponentiation. For example, if bitDepthis set equal to 16, the range is −32768˜32767; if bitDepth is set equalto 18, the range is −13107˜131071. For example, the value of the derivedmotion vector (e.g. the MVs of four 4×4 sub-blocks within one 8×8 block)is constrained such that the max difference between integer parts of thefour 4×4 sub-block MVs is no more than N pixels, such as no more than 1pixel. Here provides two methods for constraining the motion vectorbased on the bitDepth.

Method 1: remove the overflow MSB (most significant bit) by flowingoperations

$\begin{matrix}{{ux} = {\left( {{mvx} + {2{bitDepth}}} \right){\% 2}{bitDepth}}} & (1) \\{{mvx} = {{\left( {{{ux} >} = {{2bitDepth} - 1}} \right)?}\left( {{ux} - {2{bitDepth}\text{):}\mspace{14mu}{ux}}} \right.}} & (2) \\{{uy} = {\left( {{mvy} + {2{bitDepth}}} \right){\% 2}{bitDepth}}} & (3) \\{{mvy} = {\left( {{{uy} >} = {{2bitDepth} - 1}} \right)\left( {{uy} - {2{bitDepth}\text{):}\mspace{14mu}{uy}}} \right.}} & (4)\end{matrix}$

where mvx is a horizontal component of a motion vector of an image blockor a sub-block, mvy is a vertical component of a motion vector of animage block or a sub-block, and ux and uy indicates an intermediatevalue;

For example, if the value of mvx is −32769, after applying formula (1)and (2), the resulting value is 32767. In computer system, decimalnumbers are stored as two's complement. The two's complement of −32769is 1,0111,1111,1111,1111 (17 bits), then the MSB is discarded, so theresulting two's complement is 0111,1111,1111,1111 (decimal number is32767), which is same as the output by applying formula (1) and (2).

ux=(mvpx+mvdx+2bitDepth) %2bitDepth  (5)

mvx=(ux>=2bitDepth−1)?(ux−2bitdepth):ux  (6)

uy=(mvpy+mvdy+2bitDepth) %2bitDepth  (7)

mvy=(uy>=2bitDepth−1)?(uy−2bitDepth):uy  (8)

The operations may be applied during the sum of mvp and mvd, as shown informula (5) to (8).

Method 2: remove the overflow MSB by clipping the value.

vx=Clip3(−2bitDepth−1,2bitDepth−1−1,vx)

vy=Clip3(−2bitDepth−1,2bitDepth−1−1,vy)

vx is a horizontal component of a motion vector of an image block or asub-block, vy is a vertical component of a motion vector of an imageblock or a sub-block; x, y and z respectively correspond to three inputvalue of the MV clipping process, and the definition of function Clip3is as follows:

${{{Clip}3}\left( {x,y,z} \right)} = \left\{ \begin{matrix}{x;} & {z < x} \\{y;} & {z > y} \\{z;} & {otherwise}\end{matrix} \right.$

FIG. 4 is a schematic diagram of a video coding device 400 based on anembodiment of the disclosure. The video coding device 400 is suitablefor implementing the disclosed embodiments as described herein. In anembodiment, the video coding device 400 may be a decoder such as videodecoder 30 of FIG. 1A or an encoder such as video encoder 20 of FIG. 1A.

The video coding device 400 comprises ingress ports 410 (or input ports410) and receiver units (Rx) 420 for receiving data; a processor, logicunit, or central processing unit (CPU) 430 to process the data;transmitter units (Tx) 440 and egress ports 450 (or output ports 450)for transmitting the data; and a memory 460 for storing the data. Thevideo coding device 400 may also comprise optical-to-electrical (OE)components and electrical-to-optical (EO) components coupled to theingress ports 410, the receiver units 420, the transmitter units 440,and the egress ports 450 for egress or ingress of optical or electricalsignals.

The processor 430 is implemented by hardware and software. The processor430 may be implemented as one or more CPU chips, cores (e.g., as amulti-core processor), FPGAs, ASICs, and DSPs. The processor 430 is incommunication with the ingress ports 410, receiver units 420,transmitter units 440, egress ports 450, and memory 460. The processor430 comprises a coding module 470. The coding module 470 implements thedisclosed embodiments described above. For instance, the coding module470 implements, processes, prepares, or provides the various codingoperations. The inclusion of the coding module 470 therefore provides asubstantial improvement to the functionality of the video coding device400 and effects a transformation of the video coding device 400 to adifferent state. In an example, the coding module 470 is implemented asinstructions stored in the memory 460 and executed by the processor 430.

The memory 460 may comprise one or more disks, tape drives, andsolid-state drives and may be used as an over-flow data storage device,to store programs when such programs are selected for execution, and tostore instructions and data that are read during program execution. Thememory 460 may be, for example, volatile and/or non-volatile and may bea read-only memory (ROM), random access memory (RAM), ternarycontent-addressable memory (TCAM), and/or static random-access memory(SRAM).

FIG. 5 is a simplified block diagram of an apparatus 500 that may beused as either or both of the source device 12 and the destinationdevice 14 from FIG. 1 based on an exemplary embodiment.

A processor 502 in the apparatus 500 can be a central processing unit.In an example, the processor 502 can be any other type of device, ormultiple devices, capable of manipulating or processing informationnow-existing or hereafter developed. Although the disclosedimplementations can be practiced with a single processor as shown, e.g.,the processor 502, advantages in speed and efficiency can be achievedusing more than one processor.

A memory 504 in the apparatus 500 can be a read only memory (ROM) deviceor a random access memory (RAM) device in an implementation. Any othersuitable type of storage device can be used as the memory 504. Thememory 504 can include code and data 506 that is accessed by theprocessor 502 using a bus 512. The memory 504 can further include anoperating system 508 and application programs 510, the applicationprograms 510 including at least one program that permits the processor502 to perform the methods described here. For example, the applicationprograms 510 can include applications 1 through N, which further includea video coding application that performs the methods described here.

The apparatus 500 can also include one or more output devices, such as adisplay 518. The display 518 may be, in one example, a touch sensitivedisplay that combines a display with a touch sensitive element that isoperable to sense touch inputs. The display 518 can be coupled to theprocessor 502 via the bus 512.

Although depicted here as a single bus, the bus 512 of the apparatus 500can be composed of multiple buses. Further, the secondary storage 514can be directly coupled to the other components of the apparatus 500 orcan be accessed via a network and can comprise a single integrated unitsuch as a memory card or multiple units such as multiple memory cards.The apparatus 500 can thus be implemented in a wide variety ofconfigurations.

Directional intra prediction is a well-known technique that consists inpropagating the values of the neighboring samples into the predictedblock as specified by the prediction direction. FIG. 6 illustrates the93 prediction directions, where the dashed directions are associatedwith the wide-angle modes that are only applied to non-square blocks.FIG. 6 is a drawing showing angular intra prediction directions and theassociated intra-prediction modes in Versatile Video Coding Test Model 4(VTM4) and Versatile Video Coding (VVC) specification draft v. 4;

Direction could be specified by the increase of an offset betweenposition of predicted and reference sample. The larger magnitude of thisincrease corresponds to a greater skew of the prediction direction.Table 1 specifies the mapping table between predModeIntra and the angleparameter intraPredAngle. This parameter is in fact the increase of thisoffset per row (or per column) specified in the 1/32 sample resolution.

TABLE 1 Specification of intraPredAngle predModeIntra −14 −13 −12 −11−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 2 3 4 intraPredAngle 512 341 256 171 128102 86 73 64 57 51 45 39 35 32 29 26 predModeIntra 5 6 7 8 9 10 11 12 1314 15 16 17 18 19 20 21 intraPredAngle 23 20 18 16 14 12 10 8 6 4 3 2 10 −1 −2 −3 predModeIntra 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3738 intraPredAngle −4 −6 −8 −10 −12 −14 −16 −18 −20 −23 −26 −29 −32 −29−26 −23 −20 predModeIntra 39 40 41 42 43 44 45 46 47 48 49 50 51 52 5354 55 intraPredAngle −18 −16 −14 −12 −10 −8 −6 −4 −3 −2 −1 0 1 2 3 4 6predModeIntra 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72intraPredAngle 8 10 12 14 16 18 20 23 26 29 32 35 39 45 51 57 64predModeIntra 73 74 75 76 77 78 79 80 intraPredAngle 73 86 102 128 171256 341 512

Wide-angle modes could be identified by the absolute value ofintraPredAngle greater than 32 (1 sample), that corresponds to the slopeof prediction direction greater than 45 degrees.

Predicted samples (“predSamples”) could be obtained from theneighbouring samples “p” as described below:

The values of the prediction samples predSamples[x][y], with x=0 . . .nTbW−1, y=0 . . . nTbH−1 are derived as follows:

If predModeIntra is greater than or equal to 34, the following orderedsteps apply:

-   -   1. The reference sample array ref[x] is specified as follows:        -   The following applies:            -   ref[x]=p[−1−refIdx+x][−1−refIdx], with x=0 . . .                nTbW+refIdx        -   If intraPredAngle is less than 0, the main reference sample            array is extended as follows:            -   When (nTbH*intraPredAngle)>>5 is less than −1,                -   ref[x]=p[−1−refIdx][−1−refIdx+((x*invAngle+128)>>8)],                -    with x=−1 . . . (nTbH*intraPredAngle)>>5                -   ref[((nTbH*intraPredAngle)>>5)−1]                -   ref[(nTbH*intraPredAngle)>>5]                -   ref[nTbW+1+refIdx]=ref[nTbW+refIdx]        -   Otherwise,            -   ref[x]=p[−1−refIdx+x][−1−refIdx], with nTbW+1+refIdx . .                . refW+refIdx            -   ref[−1]=ref[0]        -   The additional samples ref[refW+refIdx+x] with x=1 . . .            (Max(1, nTbW/nTbH)*refIdx+1) are derived as follows:            -   ref[refW+refIdx+x]=p[−1+refW][−1−refIdx]    -   2. The values of the prediction samples predSamples[x][y], with        x=0 . . . nTbW−1, y=0 . . . nTbH−1 are derived as follows:        -   The index variable iIdx and the multiplication factor iFact            are derived as follows:            -   iIdx=((y+1+refIdx)*intraPredAngle)>>5+refIdx            -   iFact=((y+1+refIdx)*intraPredAngle) & 31        -   If cIdx is equal to 0, the following applies:            -   The interpolation filter coefficients fT[j] with j=0 . .                . 3 are derived as follows:                -   fT[j]=filterFlag? fG[iFact][j]: fC[iFact][j]            -   The value of the prediction samples predSamples[x][y] is                derived as follows:                -   predSamples[x][y]=Clip1Y(((Σ_(i=0) ³fT[i]*ref[                    x+iIdx+i])+32)>>6)        -   Otherwise (cIdx is not equal to 0), depending on the value            of iFact, the following applies:            -   If iFact is not equal to 0, the value of the prediction                samples predSamples[x][y] is derived as follows:                -   predSamples[x][y]=((32−iFact)*ref[x+iIdx+1]+iFact*ref[x+iIdx+2]+16)>>5            -   Otherwise, the value of the prediction samples                predSamples[x][y] is derived as follows:                -   predSamples[x][y]=ref[x+iIdx+1]

Otherwise (predModeIntra is less than 34), the following ordered stepsapply:

-   -   1. The reference sample array ref[x] is specified as follows:        -   The following applies:            -   ref[x]=p[−1−refIdx][−1−refIdx+x], with x=0 . . .                nTbH+refIdx        -   If intraPredAngle is less than 0, the main reference sample            array is extended as follows:            -   When (nTbW*intraPredAngle)>>5 is less than −1,                -   ref[x]=p[−1−refIdx+((x*invAngle+128)>>8)][−1−refIdx],                    with x=−1 . . . (nTbW*intraPredAngle)>>5                -   ref[((nTbW*intraPredAngle)>>5)−1]=                -   ref[(nTbW*intraPredAngle)>>5](8−145)                -   ref[nTbG+1+refIdx]=ref[nTbH+refIdx]        -   Otherwise,            -   ref[x]=p[−1−refIdx][−1−refIdx+x], with x=nTbH+1+refIdx .                . . refH+refIdx            -   ref[−1]=ref[0]        -   The additional samples ref[refH+refIdx+x] with x=1 . . .            (Max(1, nTbW/nTbH)*refIdx+1) are derived as follows:            -   ref[refH+refIdx+x]=p[−1+refH][−1−refIdx]    -   2. The values of the prediction samples predSamples[x][y], with        x=0 . . . nTbW−1, y=0 . . . nTbH−1 are derived as follows:        -   The index variable iIdx and the multiplication factor iFact            are derived as follows:            -   iIdx=((x+1+refIdx)*intraPredAngle)>>5            -   iFact=((x+1+refIdx)*intraPredAngle) & 31        -   If cIdx is equal to 0, the following applies:            -   The interpolation filter coefficients fT[j] with j=0 . .                . 3 are derived as follows: fT[j]=filterFlag?                fG[iFact][j]: fC[iFact][j]            -   The value of the prediction samples predSamples[x][y] is                derived as follows: predSamples[x][y]=Clip1Y(((Σ_(i=0)                ³fT[i]*ref[y+iIdx+i])+32)>>6)        -   Otherwise (cIdx is not equal to 0), depending on the value            of iFact, the following applies:            -   If iFact is not equal to 0, the value of the prediction                samples predSamples[x][y] is derived as follows:                -   predSamples[x][y]=((32−iFact)*ref[y+iIdx+1]+iFact*ref[y+iIdx+2]+16)>>5    -   Otherwise, the value of the prediction samples predSamples[x][y]        is derived as follows:    -   predSamples[x][y]=ref[y+iIdx+1]

The interpolation filter coefficients fC[phase][j] and fG[phase][j] withphase=0 . . . 31 and j=0 . . . 3 used in directional prediction arespecified in Table 2.

TABLE 2 Specification of interpolation filter coefficients fC and fGFractional sample fC interpolation filter coefficients fG interpolationfilter coefficients position p f_(C)[p][0] f_(C)[p][1] f_(C)[p][2]f_(C)[p][3] fG[p][0] fG[p][1] fG[p][2] fG[p][3] 0 0 64 0 0 16 32 16 0 1−1 63 2 0 15 29 17 3 2 −2 62 4 0 15 29 17 3 3 −2 60 7 −1 14 29 18 3 4 −258 10 −2 13 29 18 4 5 −3 57 12 −2 13 28 19 4 6 −4 56 14 −2 13 28 19 4 7−4 55 15 −2 12 28 20 4 8 −4 54 16 −2 11 28 20 5 9 −5 53 18 −2 11 27 21 510 −6 52 20 −2 10 27 22 5 11 −6 49 24 −3 9 27 22 6 12 −6 46 28 −4 9 2623 6 13 −5 44 29 −4 9 26 23 6 14 −4 42 30 −4 8 25 24 7 15 −4 39 33 −4 825 24 7 16 −4 36 36 −4 8 24 24 8 17 −4 33 39 −4 7 24 25 8 18 −4 30 42 −47 24 25 8 19 −4 29 44 −5 6 23 26 9 20 −4 28 46 −6 6 23 26 9 21 −3 24 49−6 6 22 27 9 22 −2 20 52 −6 5 22 27 10 23 −2 18 53 −5 5 21 27 11 24 −216 54 −4 5 20 28 11 25 −2 15 55 −4 4 20 28 12 26 −2 14 56 −4 4 19 28 1327 −2 12 57 −3 4 19 28 13 28 −2 10 58 −2 4 18 29 13 29 −1 7 60 −2 3 1829 14 30 0 4 62 −2 3 17 29 15 31 0 2 63 −1 3 17 29 15

As shown in FIG. 7 and FIG. 8, a method known as affine linear weightedprediction uses reference samples to derive values of predicted samples.For predicting the samples of a rectangular block of width W and heightH, affine linear weighted intra prediction (ALWIP) takes one line of Hreconstructed neighbouring boundary samples left of the block and oneline of W reconstructed neighbouring boundary samples above the block asinput. If the reconstructed samples are unavailable, they are generatedas it is done in the conventional intra prediction. The generation ofthe prediction signal is based on the following three steps:

1: Out of the boundary samples, four samples in the case of W=H=4 andeight samples in all other cases are extracted by averaging.

2: A matrix vector multiplication, followed by addition of an offset, iscarried out with the averaged samples as an input. The result is areduced prediction signal on a subsampled set of samples in the originalblock.

3: The prediction signal at the remaining positions is generated fromthe prediction signal on the subsampled set by linear interpolation,which is a single step linear interpolation in each direction.

The matrices and offset vectors needed to generate the prediction signalare taken from three sets S₀, S₁, S₂ of matrices. The set S₀ consists of18 matrices A₀ ^(i), iϵ{0, . . . , 17} each of which has 16 rows and 4columns and 18 offset vectors b₀ ^(i), iϵ{0, . . . , 17} each of size16. Matrices and offset vectors of that set are used for blocks of size4×4. The set S₁ consists of 10 matrices A₁ ^(i), iϵ{0, . . . , 9}, eachof which has 16 rows and 8 columns and 10 offset vectors b₁ ^(i), iϵ{0,. . . , 9} each of size 16. Matrices and offset vectors of that set areused for blocks of sizes 4×8, 8×4 and 8×8. Finally, the set S₂ consistsof 6 matrices A₂ ^(i), iϵ{0, . . . ,5}, each of which has 64 rows and 8columns and of 6 offset vectors b₂ ^(i), iϵ{0, . . . , 5} of size 64.Matrices and offset vectors of that set or parts of these matrices andoffset vectors are used for all other block-shapes.

The total number of multiplications needed in the computation of thematrix vector product is always smaller than or equal to 4·W·H. In otherwords, at most four multiplications per sample are required for theALWIP modes.

Averaging of the Boundary

In a first step, the input boundaries bdry^(top) and bdry^(left) arereduced to smaller boundaries bdry_(red) ^(top) and bdry_(red) ^(left).Here, bdry_(red) ^(top) and bdry_(red) ^(left) both consists of 2samples in the case of a 4×4-block and both consist of 4 samples in allother cases.

In the case of a 4×4-block, for 0≤i<2, one defines bdry_(red)^(top)[i]=((Σ_(j=0) ¹bdry^(top)[i·2+j])+1)>>1 and defines bdry_(red)^(left) analogously.

Otherwise, if the block-width W is given as W=4·2^(k), for 0≤i<4, onedefines bdry_(red) ^(top)[i]=((Σ_(j=0) ² ^(k)⁻¹bdry^(top)[i·2^(k)+j])(1<<(k−1)))>>k and defines bdry_(red) ^(left)analogously.

The two reduced boundaries bdry_(red) ^(top) and bdry_(red) ^(left) areconcatenated to a reduced boundary vector bdry_(red) which is thus ofsize four for blocks of shape 4×4 and of size eight for blocks of allother shapes. If mode refers to the ALWIP-mode, this concatenation isdefined as follows:

${bdry_{red}} = \left\{ \begin{matrix}\left\lbrack {{bdry_{red}^{top}}\ ,\ {bdry_{red}^{left}}} \right\rbrack & {{{for}\mspace{14mu} W} = {H = {{4\mspace{14mu}{and}\mspace{14mu}{mode}} < 18}}} \\\left\lbrack {{{bdr}y_{red}^{left}},\ {{bdr}y_{red}^{top}}} \right\rbrack & {{{for}\mspace{14mu} W} = {H = {{4\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 18}}} \\\left\lbrack {{bdry_{red}^{Cop}}\ ,\ {bdry_{red}^{left}}} \right\rbrack & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} = {{8\mspace{14mu}{and}\mspace{14mu}{mode}} < 10}} \\\left\lbrack {{bdry_{red}^{left}},\ {bdry_{red}^{top}}} \right\rbrack & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} = {{8\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 10}} \\\left\lbrack {{bdry_{red}^{top}}\ ,\ {bdry_{red}^{left}}} \right\rbrack & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > {8\mspace{14mu}{and}\mspace{14mu}{mode}} < 6} \\\left\lbrack {{bdry_{red}^{left}},\ {bdry_{red}^{top}}} \right\rbrack & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > {8\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 6.}\end{matrix} \right.$

Finally, for the interpolation of the subsampled prediction signal, onlarge blocks a second version of the averaged boundary is needed.Namely, if min(W, H)>8 and W≥H, one writes W=8*2^(l), and, for 0≤i<8,defines bdry_(redII) ^(top)=((Σ_(j=0) ² ^(l) ⁻¹bdry^(top)[i·2^(l)+j])+(1<<(l−1)))>>l. If min(W, H)>8 and H>W, onedefines bdry_(redII) ^(left) analogously.

Generation of the reduced prediction signal by matrix vectormultiplication

Out of the reduced input vector bdry_(red) one generates a reducedprediction signal pred_(red). The latter signal is a signal on thedownsampled block of width W_(red) and height H_(red). Here, W_(red) andH_(red) are defined as:

$W_{red} = \left\{ {{\begin{matrix}4 & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} \leq 8} \\{\min\left( {W,8} \right)} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > 8}\end{matrix}H_{red}} = \left\{ \begin{matrix}4 & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} \leq 8} \\{\min\left( {H,8} \right)} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > 8}\end{matrix} \right.} \right.$

The reduced prediction signal pred_(red) is computed by calculating amatrix vector product and adding an offset:

pred_(red) =A·bdry_(red) +b.

Here, A is a matrix that has W_(red)·H_(red) rows and 4 columns if W=H=4and 8 columns in all other cases. b is a vector of size W_(red)·H_(red).

The matrix A and the vector b are taken from one of the sets S₀, S₁, S₂as follows. One defines an index (further referred to as block sizetype) idx=idx(W,H) as follows:

${id{x\left( {W,H} \right)}} = \left\{ \begin{matrix}{{0\mspace{14mu}{for}\mspace{14mu} W} = {H = 4}} \\{{1\mspace{9mu}{for}\mspace{14mu}\max\mspace{14mu}\left( {W,H} \right)} = 8} \\{{2\mspace{9mu}{for}\mspace{14mu}{\max\left( {W,H} \right)}} > {8.}}\end{matrix} \right.$

Moreover, one puts m as follows:

$m = \left\{ \begin{matrix}{mode} & {{{for}\mspace{14mu} W} = {H = {{4\mspace{14mu}{and}\mspace{14mu}{mode}} < 18}}} \\{{mode} - 17} & {{{for}\mspace{14mu} W} = {H = {{4\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 18}}} \\{mode} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} = {{8\mspace{14mu}{and}\mspace{14mu}{mode}} < 10}} \\{{mode} - 9} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} = {{8\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 10}} \\{mode} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > {8\mspace{14mu}{and}\mspace{14mu}{mode}} < 6} \\{{mode} - 5} & {{{for}\mspace{14mu}{\max\left( {W,H} \right)}} > {8\mspace{14mu}{and}\mspace{14mu}{mode}} \geq 6.}\end{matrix} \right.$

Then, if idx≤1 or idx=2 and min(W,H)>4, one puts A=A_(idx) ^(m) andb=b_(idx) ^(m). In the case that idx=2 and min(W,H)=4, one lets A be thematrix that arises by leaving out every row of A_(idx) ^(m) that, in thecase W=4, corresponds to an odd x-coordinate in the downsampled block,or, in the case H=4, corresponds to an odd y-coordinate in thedownsampled block.

Finally, the reduced prediction signal is replaced by its transpose inthe following cases:

-   -   W=H=4 and mode ≥18    -   max(W, H)=8 and mode ≥10    -   max(W, H)>8 and mode ≥6

Technical problem to be solved.

In ALWIP, predicted samples are obtained using convolution with a set ofcoefficients. Notably, the reduced prediction signal pred_(red) iscomputed by calculating a matrix vector product and adding an offsetbased on pred_(red)=A·bdry_(red)+b.

If to juxtapose this step with the interpolation step used inskew-directional intra prediction, (predSamples[x][y]=Clip1Y(((Σ_(i=0)³fT[ . . . ]*ref[y+iIdx . . . i])+32)>>6)), some similarities could benoticed.

Firstly, multiplication is performed for a set of reference samples thatare obtained from the neighboring ones using reference sample filtering.Secondly, predicted samples are obtained from the reference ones usingconvolution operation. The difference between these two methods is thatthe convolution cores (A and fT[ ]) are different. Hence, despite thesimilarities, the steps for these two methods are different and requireseparate hardware designs with similar modules.

Solution and Advantages. The present disclosure proposes a unifieddirectional intra prediction with ALWIP by aligning accuracy ofmultiplication operations. This unification enables a possibility tohave a unified convolution step for the both methods and thus toeliminate hardware redundancy.

The core of the present disclosure could be formulated as an intraprediction method comprising the following steps. The steps arepreparing a set of reference samples; obtain predicted signal byconvolving reference samples with a set of coefficients that could bedefined adaptively per a position of predicted sample, upsample thepredicted signal. Each of these steps has parameters that could beadjusted. By defining a set of parameters, the sequence of steps mayoperate as ALWIP or as directional intra prediction.

FIG. 7 shows the flowchart applicable to both methods ALWIP anddirectional intra prediction. All of the steps shown in FIG. 7 have thesame input and output data, but processing within each of the stepvaries depending on what intra prediction method is selected.

The first step of reference sample generation is performed as boundaryaveraging in case of ALWIP and samples selection and conditionalfiltering in case of directional intra prediction

The second step of convolving reference samples with a convolution corerequire that both methods use the same precision of filter cores, anddesirably, the same number of coefficients.

The last step of upsampling may be skipped for the case of directionalintra prediction. The design implies certain constraints on theparameters used by the both methods.

Particularly, a set of coefficients should comprise coefficients of thegiven precision (i.e. bit-depth).

In one embodiment, coefficients of the directional interpolation filtersare defined in the same precision of the coefficients belonging to thematrix “A”. For example, this set may be defined as it is given in Table3.

TABLE 3 Intra prediction interpolation filter coefficients SubpixelCubic filter Gauss filter offset c₀ c₁ c₂ c₃ c₀ c₁ c₂ c₃  0 (integer) 0256 0 0 47 161 47 1  1 −3 252 8 −1 43 161 51 1  2 −5 247 17 −3 40 160 542  3 −7 242 25 −4 37 159 58 2  4 −9 236 34 −5 34 158 62 2  5 −10 230 43−7 31 156 67 2  6 −12 224 52 −8 28 154 71 3  7 −13 217 61 −9 26 151 76 3 8 −14 210 70 −10 23 149 80 4  9 −15 203 79 −11 21 146 85 4 10 −16 19589 −12 19 142 90 5 11 −16 187 98 −13 17 139 94 6 12 −16 179 107 −14 16135 99 6 13 −16 170 116 −14 14 131 104 7 14 −17 162 126 −15 13 127 108 815 −16 153 135 −16 11 123 113 9 16 (half-pel) −16 144 144 −16 10 118 11810 17 −16 135 153 −16 9 113 123 11 18 −15 126 162 −17 8 108 127 13 19−14 116 170 −16 7 104 131 14 20 −14 107 179 −16 6 99 135 16 21 −13 98187 −16 6 94 139 17 22 −12 89 195 −16 5 90 142 19 23 −11 79 203 −15 4 85146 21 24 −10 70 210 −14 4 80 149 23 25 −9 61 217 −13 3 76 151 26 26 −852 224 −12 3 71 154 28 27 −7 43 230 −10 2 67 156 31 28 −5 34 236 −9 2 62158 34 29 −4 25 242 −7 2 58 159 37 30 −3 17 247 −5 2 54 160 40 31 −1 8252 −3 1 51 161 43

In another embodiment, coefficients of matrix A have a 6-bit precisionin order 10-bit samples processing fits in 16-bit arithmetic. In otherwords, the coefficients of the matrix A have a 6-bit precision such thatprocessing of 10-bit samples fits in a 16-bit arithmetic.

ALWIP method could be also referred to as matrix-based intra prediction(MIP). Signaling of an intra prediction mode in presence of MIP could beformulated as it is shown in Table 4.

TABLE 4 Signaling of intra_prediction modes if MIP is enabled.  ... if(treeType = = SINGLE_TREE || treeType = = DUAL_TREE_LUMA ) {  if( Abs(Log2( cbWidth ) - Log2( cbHeight) ) <= 2)   intra_lwip_flag[ x0 ][ y0]ae(v)  if( intra_lwip_flag[ x0 ][ y0 ] ) {   intra_lwip_mpm_flag[ x0 ][y0 ] ae(v)   if( intra_lwip_mpm_flag[ x0 ][ y0 ] )   intra_lwip_mpm_idx[ x0 ][ y0 ] ae(v)   else   intra_lwip_mpm_remainder [ x0 ][ y0 ] ae(v)  } else {   if( ( y0 %CtbSizeY ) > 0)    intra_luma_ref_idx[ x0 ][ y0 ] ae(v)   if(intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&    ( cbWidth <= MaxTbSizeY ||cbHeight <= MaxTbSizeY ) &&    ( cbWidth * cbHeight > MinTbSizeY *MinTbSizeY ))    intra_subpartitions_mode_flag[ x0 ][ y0 ] ae(v)   if(intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&    cbWidth <=MaxTbSizeY && cbHeight <= MaxTbSizeY )   intra_subpartitions_split_flag[ x0 ][ y0 ] ae(v)   if(intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&   intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0)   intra_luma_mpm_flag[ x0 ][ y0 ] ae(v)   if( intra_luma_mpm_flag[ x0][ y0 ] )    intra_luma_mpm_idx[ x0 ][ y0 ] ae(v)   else   intra_luma_mpm_remainder [ x0 ][ y0 ] ae(v)  } ...

The process of MPM list derivation requires intra prediction modes ofthe neighboring blocks. However, even if MIP is not used for the currentblock, neighboring blocks may be predicted using MIP and thus would havean intra prediction mode that is inconsistent with conventional non-MIPintra prediction modes. For this purpose a lookup table is introduced(Tables 4-6), that maps input MIP mode indexes to conventional intraprediction modes.

TABLE 5 A mode mapping lookup table for blocks 4 × 4 MIP index 0 1 2 3 45 6 7 8 9 10 11 12 13 14 15 16 17 intraPredMode 0 18 18 0 18 0 12 0 18 218 12 18 18 1 18 18 0 MIP index 18 19 20 21 22 23 24 25 26 27 28 29 3031 32 33 34 intraPredMode 0 50 0 50 0 56 0 50 66 50 56 50 50 1 50 50 50

TABLE 6 A mode mapping lookup table for blocks 8 × 8 MIP index 0 1 2 3 45 6 7 8 9 10 11 12 13 14 15 16 17 18 intraPredMode 0 1 0 1 0 22 18 18 10 1 0 1 0 44 0 50 1 0

TABLE 7 A mode mapping lookup table for blocks 16 × 16 MIP index 0 1 2 34 5 6 7 8 9 10 intraPredMode 1 1 1 1 18 0 1 0 1 50 0

When a MIP block is predicted, its MPM list is being constructed withconsideration of the neighboring non-MIP modes. These modes are mappedto the MIP ones using two steps.

At the first step, directional intra prediction mode is mapped to thereduced set of directional modes (see Table 8)

The second step is to determine MIP mode based on the determineddirectional mode of the reduced set of directional modes.

TABLE 8 Mapping of the directional intra prediction modes to the reducedset of directional modes intraPredMode 0 1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 17 intraPredMode33 0 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9intraPredMode 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35intraPredMode33 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18intraPredMode 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53intraPredMode33 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27intraPredMode 54 55 56 57 58 59 60 61 62 63 64 65 66 67 intraPredMode3328 28 29 29 30 30 31 31 32 32 33 33 34 DM_CHROMA_IDX

As shown in FIG. 9, MIP coefficients (elements of matrices A₀ ^(i), A₁^(i) and A₂ ^(i)) has the length of 10 bits including 9-bit magnitudeand a sign (1 bit). Values of MIP coefficients used in the referencesoftware VTM-5.0 and the H.266/VVC spec draft, have the statisticspresented in Table 9.

TABLE 9 Statistics of MIP coefficients Block size Values Ranges 4 × 4−222 ... 435 657 8 × 8 −207 ... 476 683 16 × 16 −170 ... 314 484

In the proposed present disclosure, the magnitude of MIP coefficients isaligned with the magnitude of filter coefficients used for interpolationfiltering in intra prediction. This alignment enables reusingmultipliers for intra-prediction interpolation filtering by MIP inmatrix multiplication. To achieve it, magnitudes of MIP coefficientsshould not exceed 6 bits. As shown in FIG. 10, 6-bit magnitudes of MIPcoefficients are extracted from 9-bit magnitude 1001 subject to theposition of a non-zero most significant bit (MSB). 4 cases denoted by1002-1005 are available. To restore 9-bit magnitude Gm. and sign of anMIP coefficient, the following formula can be usedC_(MIP)=v_(sgn)·(q<<s), where q is 6-bit magnitude of an MIPcoefficient; s is a left shift value; v_(sgn) is a sign value of an MIPcoefficient. Left shift values subject to the position of a mostsignificant bit are presented in Table 10.

TABLE 10 Left shift valuessubject to the position of a most significantbit Case index in FIG. 10 Left shift value 1002 0 1003 1 1004 2 1005 3

The representation of a MIP coefficient with 6-bit magnitude 1102 isshown in FIG. 11. At the left most position, a MIP coefficient sign 1101is placed. 2-bit value of left shift is appended to the MIP coefficientmagnitude. In FIG. 12, it is shown how to reuse multipliers forintra-prediction interpolation filtering by MIP. 6-bit magnitude 1202 ofa MIP coefficient and pixel value 1203 (that has, for example, bit-depthof 10 bits) are inputs of multiplier 1204 that provides results withmagnitude 1205 that is prepended by sign 1206 that has the same value assign 1201 of the MIP coefficient.

Multiplication operation in matrix multiplication is performed withreduced bit depth by repositioning shift operation after multiplicationp·C_(MIP)=v_(sgn)·((p·q)<<s), where q is a magnitude of the MIPcoefficient; s is a left shift value; v_(sg)n is a sign value of the MIPcoefficient; p is a reference sample, p=bdry_(red) ^(top)[i]0≤i<W; orp=bdry_(red) ^(left)[i], 0≤i<H.

Array 7. Exemplary values of MIP coefficients selected based on theproposed method

  const short mipMatrix4x4round_const[18][16][4] = {  {   { 132 , −14 ,144 , −14 },   { 160 , 68 , 5 , 24 },   { −32 , 272 , −9 , 30 },   { −66, 248 , 9 , 10 },   { −5 , 17 , 192 , 60 },   { 2 , 124 , 9 , 124 },   {−60 , 192 , −40 , 96 },   { −18 , 112 , −36 , 64 },   { −12 , 28 , −28 ,272 },   { −36 , 80 , −56 , 192 },   { −24 , 80 , −28 , 80 },   { −14 ,72 , −24 , 72 },   { 3 , 10 , −56 , 240 },   { −33 , 68 , −12 , 96 },  { −24 , 72 , −9 , 66 },   { −18 , 72 , −17 , 66 }  },  {   { 32 , −10, 224 , 6 },   { 136 , −36 , 144 , 7 },   { 96 , 124 , 34 , −1 },   { −9, 272 , −10 , −4 },   { −9 , 3 , 264 , −7 },   { −18 , −8 , 288 , −18 },  { −4 , −9 , 264 , −15 },   { −120 , 192 , 160 , −5 },   { 4 , −6 , 96, 160 },   { 3 , −10 , 48 , 192 },   { 7 , −36 , 12 , 224 },   { −34 ,−15 , −4 , 240 },   { 0 , −15 , −126 , 384 },   { 0 , −24 , −126 , 384},   { 0 , −24 , −124 , 320 },   { 16 , −34 , −112 , 320 }  },  {   {160 , 14 , 112 , −40 },   { 248 , −6 , 33 , −34 },   { 224 , 40 , 16 ,−28 },   { −80 , 320 , 5 , −20 },   { −56 , 3 , 264 , 40 },   { −6 , 14, 192 , 24 },   { 96 , 7 , 72 , 17 },   { −56 , 224 , −24 , 12 },   { −6, −3 , 1 , 264 },   { −24 , 0 , 12 , 256 },   { −15 , −7 , 16 , 240 },  { −40 , 40 , −20 , 224 },   { −2 , 3 , 6 , 248 },   { −4 , 4 , 6 , 248},   { −5 , 2 , 12 , 248 },   { −1 , −12 , 17 , 248 }  },  {   { 40 , −6, 248 , −28 },   { 224 , −17 , 48 , −2 },   { 96 , 192 , −36 , 2 },   {−32 , 272 , 4 , 8 },   { −9 , 9 , 192 , 64 },   { 48 , −20 , 160 , 64 },  { 96 , 112 , −10 , 56 },   { −5 , 272 , −48 , 20 },   { 3 , 5 , 24 ,224 },   { 3 , −8 , 36 , 224 },   { −17 , 40 , 68 , 160 },   { −72 , 224, 20 , −8 },   { −3 , 0 , 4 , 252 },   { 6 , 0 , 2 , 248 },   { −15 , −9, 40 , 224 },   { −192 , 80 , 192 , −33 }  },  {   { 96 , −18 , 240 ,−68 },   { 48 , 63 , 160 , −24 },   { −48 , 192 , 40 , 48 },   { −20 ,192 , −72 , 120 },   { −48 , 3 , 160 , 136 },   { −48 , 2 , 64 , 224 },  { −28 , 1 , 14 , 248 },   { −14 , 1 , −6 , 256 },   { 3 , 1 , −17 ,264 },   { 0 , 1 , −12 , 264 },   { −5 , 5 , 2 , 248 },   { −9 , 4 , 7 ,248 },   { −6 , 1 , 8 , 248 },   { −7 , 2 , 7 , 248 },   { −10 , 5 , 6 ,248 },   { −10 , 5 , 4 , 248 }  },  {   { 68 , 1 , 192 , −3 },   { 192 ,−15 , 72 , 3 },   { 272 , −20 , −1 , 1 },   { 160 , 96 , −3 , 2 },   {−14 , −2 , 288 , −17 },   { 2 , 3 , 264 , −15 },   { 96 , −3 , 160 , −3},   { 224 , −28 , 56 , 0 },   { 2 , 0 , 144 , 112 },   { −1 , −5 , 240, 20 },   { −15 , −1 , 288 , −18 },   { 20 , 2 , 248 , −18 },   { 4 , −1, −36 , 288 },   { 3 , −7 , 20 , 240 },   { 6 , −7 , 112 , 144 },   { 1, −3 , 192 , 56 }  },  {   { 144 , −10 , 136 , −10 },   { 112 , 80 , 80, −16 },   { −6 , 240 , 40 , −20 },   { −20 , 264 , 9 , 0 },   { −72 ,12 , 288 , 24 },   { −96 , 63 , 224 , 60 },   { −132 , 160 , 96 , 132 },  { −72 , 192 , −48 , 160 },   { −15 , −4 , 36 , 240 },   { −24 , 20 ,−40 , 288 },   { −30 , 48 , −62 , 240 },   { −34 , 62 , −40 , 160 },   {20 , 20 , −96 , 288 },   { 1 , 40 , −60 , 192 },   { −8 , 56 , −24 , 112},   { −12 , 62 , −9 , 96 }  },  {   { 192 , 9 , 80 , −20 },   { 272 ,−10 , −12 , 1 },   { 224 , 28 , 2 , 5 },   { −20 , 272 , −2 , 0 },   { 0, 1 , 256 , −1 },   { 144 , 7 , 120 , −20 },   { 288 , −28 , 9 , −20 },  { 160 , 96 , 9 , −18 },   { −15 , −2 , 48 , 224 },   { −15 , −5 , 80 ,192 },   { 112 , −8 , 9 , 132 },   { 256 , −28 , −72 , 72 },   { 5 , 2 ,−16 , 264 },   { −3 , 1 , −17 , 272 },   { −8 , −2 , −14 , 272 },   { 96, −30 , −96 , 256 }  },  {   { 192 , −40 , 132 , −36 },   { 288 , −48 ,36 , −34 },   { 68 , 192 , 10 , −28 },   { −15 , 264 , 20 , −24 },   {−56 , 9 , 256 , 40 },   { 48 , −36 , 192 , 24 },   { 68 , 40 , 66 , 20},   { −48 , 240 , −36 , 15 },   { −12 , 1 , 1 , 264 },   { −20 , −1 , 8, 256 },   { −12 , −18 , 7 , 248 },   { −120 , 136 , −48 , 224 },   { −3, 3 , 7 , 248 },   { −5 , 5 , 8 , 248 },   { 0 , −2 , 9 , 252 },   { −36, 24 , 16 , 248 }  },  {   { −40 , 96 , 264 , −60 },   { −96 , 160 , 136, 56 },   { −60 , 96 , 56 , 160 },   { −14 , 30 , 15 , 224 },   { −56 ,18 , 68 , 224 },   { −3 , −15 , 8 , 264 },   { 5 , −20 , 12 , 264 },   {−2 , −7 , 20 , 252 },   { 7 , −2 , −4 , 256 },   { −2 , 3 , 14 , 248 },  { −7 , 8 , 14 , 248 },   { −5 , 7 , 14 , 248 },   { −4 , 3 , 15 , 248},   { −4 , 2 , 14 , 252 },   { −3 , 3 , 12 , 252 },   { −2 , 3 , 16 ,248 }   },  {   { 144 , −28 , 240 , −112 },   { 240 , −112 , 224 , −112},   { 320 , −160 , 192 , −112 },   { 320 , −160 , 192 , −120 },   { −40, −72 , 256 , 112 },   { −17 , −96 , 256 , 112 },   { 36 , −144 , 256 ,96 },   { 112 , −224 , 256 , 96 },   { 14 , −12 , −16 , 272 },   { 12 ,−8 , −10 , 264 },   { 2 , 0 , −4 , 264 },   { 1 , −6 , 9 , 264 },   { −4, 0 , 24 , 240 },   { 2 , −6 , 28 , 240 },   { 7 , −12 , 28 , 240 },   {12 , −15 , 30 , 240 }  },  {   { 36 , −15 , 240 , 3 },   { 96 , 24 , 144, −2 },   { 36 , 224 , 18 , −24 },   { −1 , 264 , 3 , −14 },   { −10 , 2, 256 , 2 },   { −28 , 1 , 252 , 28 },   { −68 , 112 , 132 , 80 },   {−48 , 240 , −80 , 120 },   { −3 , −10 , 48 , 224 },   { −2 , −5 , −24 ,272 },   { −30 , 17 , −48 , 256 },   { −48 , 80 , −68 , 160 },   { 2 ,14 , −112 , 320 },   { 5 , 28 , −72 , 192 },   { 16 , 28 , −33 , 96 },  { 12 , 30 , −17 , 80 }  },  {   { 24 , 2 , 224 , 7 },   { 2 , 30 , 224, 2 },   { −20 , 80 , 192 , 1 },   { −34 , 96 , 192 , −2 },   { −28 , 20, 264 , −1 },   { −34 , 28 , 264 , 1 },   { −36 , 28 , 264 , 5 },   {−40 , 33 , 264 , 6 },   { −15 , 15 , 240 , 24 },   { −20 , 24 , 248 , 10},   { −30 , 33 , 248 , 5 },   { −36 , 40 , 240 , −10 },   { 9 , −18 ,−240 , 480 },   { 6 , −24 , −224 , 448 },   { −7 , −17 , −124 , 288 },  { −17 , −6 , −72 , 192 }  },  {   { 24 , −12 , 240 , 8 },   { 80 , −30, 192 , 15 },   { 34 , 72 , 144 , 9 },   { −96 , 256 , 96 , 1 },   { −7, 6 , 264 , −8 },   { −16 , 6 , 272 , −8 },   { −1 , −14 , 272 , −2 },  { −48 , 40 , 264 , 1 },   { 7 , 14 , 160 , 112 },   { 10 , 9 , 192 ,72 },   { 9 , 12 , 192 , 56 },   { 18 , −8 , 224 , 28 },   { −5 , −33 ,−96 , 320 },   { −2 , −56 , −96 , 320 },   { 0 , −56 , −80 , 288 },   {−5 , −48 , −63 , 264 }  },  {   { 72 , 8 , 192 , −18 },   { −33 , 192 ,112 , −9 },   { −66 , 264 , −24 , 96 },   { 48 , 144 , −144 , 192 },   {−112 , 120 , 192 , 72 },   { −36 , 144 , −40 , 192 },   { 96 , 24 , −192, 272 },   { 96 , −20 , −192 , 264 },   { 16 , 24 , −80 , 288 },   { 62, −40 , −160 , 288 },   { 48 , −48 , −144 , 240 },   { 40 , −31 , −144 ,224 },   { 33 , −40 , −112 , 272 },   { 24 , −48 , −112 , 224 },   { 18, −40 , −120 , 224 },   { 24 , −36 , −128 , 224 }  },  {   { 24 , 2 ,224 , 8 },   { 3 , 28 , 224 , 3 },   { −18 , 80 , 192 , 1 },   { −28 ,96 , 192 , −4 },   { −24 , 17 , 264 , −2 },   { −30 , 24 , 264 , 1 },  { −31 , 24 , 264 , 2 },   { −32 , 28 , 256 , 4 },   { −8 , 16 , 224 ,34 },   { −18 , 24 , 248 , 10 },   { −28 , 32 , 248 , 5 },   { −32 , 40, 240 , −10 },   { 5 , −10 , −224 , 448 },   { −1 , −9 , −192 , 384 },  { −14 , −9 , −112 , 264 },   { −28 , −6 , −68 , 192 }  },  {   { 14 ,−7 , 288 , −48 },   { 9 , −17 , 320 , −62 },   { −14 , 14 , 288 , −40 },  { −192 , 192 , 264 , −17 },   { −15 , 12 , 160 , 96 },   { −14 , 8 ,128 , 132 },   { 1 , −14 , 72 , 192 },   { 14 , −17 , 56 , 192 },   { 3, −1 , −12 , 264 },   { 4 , −1 , −14 , 264 },   { −4 , 4 , −12 , 264 },  { 3 , −2 , −4 , 256 },   { −3 , 0 , 7 , 248 },   { −3 , −2 , 8 , 248},   { −4 , −1 , 7 , 248 },   { −7 , 1 , 7 , 248 }  },  {   { −24 , −4 ,288 , −4 },   { −18 , −12 , 288 , −2 },   { −2 , −28 , 288 , −2 },   {−2 , −24 , 288 , −5 },   { 17 , 0 , 240 , 1 },   { 14 , 3 , 240 , 1 },  { 15 , 9 , 224 , 7 },   { 18 , 1 , 224 , 12 },   { 2 , −2 , 8 , 248 },  { 2 , −1 , 7 , 248 },   { 1 , 1 , 2 , 252 },   { −1 , 3 , 2 , 252 },  { 1 , 1 , −10 , 264 },   { 0 , 2 , −10 , 264 },   { 1 , 1 , −10 , 264},   { 1 , 1 , −10 , 264 }  } };

Array 8. Exemplary values of MIP coefficients selected based on theproposed method, defined in C/C++ programming language.

const short mipMatrix8x8round_const[10][16][8] = {  {   { 40 , −28 , 8 ,−1 , 272 , −40 , 7 , −2 },   { 192 , −32 , −4 , 1 , 132 , −40 , 12 , −4},   { 128 , 144 , −20 , −3 , 10 , −5 , 2 , −1 },   { 14 , 136 , 112 , 0, −9 , 7 , −3 , −1 },   { −12 , 2 , −2 , 1 , 36 , 264 , −40 , 6 },   {−34 , 0 , 2 , 1 , 192 , 128 , −40 , 7 },   { 48 , −40 , 8 , 1 , 256 ,−14 , −2 , 0 },   { 132 , 14 , −18 , 4 , 160 , −40 , 10 , −5 },   { 3 ,−1 , 0 , 1 , −16 , 32 , 272 , −36 },   { 10 , −1 , 0 , 2 , −48 , 192 ,132 , −30 },   { −14 , 5 , −4 , 2 , 12 , 272 , −12 , −4 },   { −14 , −5, 4 , 4 , 136 , 160 , −34 , 5 },   { −4 , −1 , −2 , 1 , 4 , −15 , 24 ,248 },   { −3 , 2 , −1 , 4 , 17 , −56 , 192 , 96 },   { 1 , −1 , −3 , 2, −7 , 7 , 264 , −8 },   { 4 , −1 , −4 , 3 , −30 , 144 , 160 , −20 }, },  {   { 5 , 192 , −40 , 5 , −48 , 80 , 72 , −8 },   { −9 , 8 , 240 ,−14 , 9 , −36 , 18 , 40 },   { 3 , −4 , 7 , 248 , 0 , 1 , −18 , 20 },  { 2 , 3 , −34 , 288 , 3 , −3 , −1 , 0 },   { −24 , 56 , 96 , −20 , 14, −66 , 126 , 72 },   { 6 , −24 , 80 , 160 , 1 , 9 , −40 , 63 },   { 3 ,7 , −48 , 288 , 3 , −2 , −1 , 6 },   { 2 , 4 , −33 , 288 , 3 , −4 , 0 ,0 },   { −12 , −20 , 80 , 72 , 3 , 7 , −66 , 192 },   { −1 , −7 , −28 ,272 , 3 , 4 , −5 , 17 },   { 2 , 2 , −36 , 288 , 3 , −3 , 3 , −1 },   {1 , 4 , −32 , 288 , 4 , −4 , 1 , −1 },   { −7 , −31 , 8 , 192 , 7 , 20 ,−16 , 80 },   { −4 , −3 , −40 , 288 , 4 , 3 , −2 , 10 },   { 2 , 2 , −34, 288 , 4 , −3 , 4 , −4 },   { 3 , 7 , −28 , 272 , 7 , −2 , 2 , 1 },  }, {   { 144 , 36 , −5 , 1 , 8 , 72 , −2 , 3 },   { −63 , 272 , 15 , −4 ,−17 , 40 , 6 , 5 },   { −4 , −48 , 288 , 4 , −24 , 24 , 8 , 8 },   { 0 ,10 , −80 , 320 , −14 , 7 , 2 , −1 },   { 96 , 16 , 0 , −2 , −96 , 192 ,56 , −4 },   { −66 , 272 , −8 , 0 , −96 , 96 , 48 , 9 },   { −18 , −24 ,288 , −12 , −60 , 31 , 32 , 14 },   { −4 , 2 , −80 , 320 , −24 , −2 , 10, 6 },   { 72 , 6 , 4 , −1 , −72 , 8 , 192 , 48 },   { −80 , 264 , −20 ,1 , −112 , 31 , 112 , 60 },   { −34 , −1 , 272 , −24 , −80 , 24 , 31 ,56 },   { −7 , −5 , −68 , 288 , −36 , 4 , −16 , 40 },   { 56 , 3 , 7 ,−1 , −48 , 5 , −31 , 264 },   { −80 , 240 , −24 , 0 , −96 , 7 , −16 ,224 },   { −48 , 24 , 240 , −28 , −80 , 5 , −24 , 144 },   { −15 , −14 ,−48 , 264 , −40 , −5 , −40 , 80 },  },  {   { 224 , −48 , 10 , −1 , 384, −72 , 15 , −2 },   { 448 , 96 , −48 , 6 , 24 , −15 , 2 , −3 },   { −2, 480 , 80 , −36 , −6 , −3 , 0 , −4 },   { −1 , −18 , 480 , 60 , 3 , −6, −1 , −5 },   { −48 , 0 , −5 , −2 , 256 , 384 , −80 , 6 },   { 124 ,−36 , 3 , 1 , 448 , −24 , −9 , 0 },   { 384 , 56 , −36 , 7 , 124 , −31 ,4 , −4 },   { 112 , 384 , 18 , −10 , 5 , −2 , 3 , −4 },   { 3 , −2 , −2, −1 , −63 , 264 , 384 , −72 },   { −28 , 1 , −6 , −3 , 112 , 480 , −31, −15 },   { 48 , −30 , −5 , −3 , 448 , 96 , −40 , −5 },   { 288 , 20 ,−12 , 7 , 224 , −17 , −2 , −5 },   { 1 , −1 , 0 , 0 , 28 , −96 , 288 ,288 },   { 1 , −1 , −6 , −3 , −31 , 96 , 480 , −30 },   { −18 , −2 , −8, −2 , 36 , 448 , 68 , −16 },   { 30 , −3 , 0 , 3 , 288 , 192 , −10 , 1},  },  {   { −48 , 36 , 6 , 24 , 120 , 144 , −33 , 7 },   { −28 , 24 ,31 , 56 , −16 , 224 , −36 , 0 },   { −4 , 8 , 3 , 132 , −112 , 224 , 12, −10 },   { 8 , 4 , −28 , 192 , −144 , 160 , 64 , −7 },   { 6 , 3 , 0 ,24 , −68 , 160 , 160 , −31 },   { −4 , 8 , −2 , 60 , −68 , 40 , 240 ,−24 },   { −7 , 16 , −24 , 96 , −72 , −36 , 240 , 33 },   { −6 , 18 ,−20 , 120 , −80 , −62 , 160 , 112 },   { −2 , 4 , −1 , 20 , −18 , −40 ,160 , 128 },   { −8 , 9 , −8 , 48 , −40 , −17 , 36 , 224 },   { −10 , 12, −20 , 80 , −64 , −2 , −48 , 288 },   { −10 , 14 , −16 , 96 , −80 , 3 ,−68 , 288 },   { −5 , 1 , −5 , 20 , −17 , 8 , −80 , 320 },   { −15 , 5 ,−12 , 48 , −33 , −6 , −80 , 320 },   { −20 , 4 , −14 , 63 , −48 , −18 ,−68 , 320 },   { −20 , 7 , −12 , 80 , −56 , −20 , −56 , 288 },  },  {  { −12 , −16 , 6 , 0 , 288 , −10 , 0 , −1 },   { 80 , −28 , −9 , 3 ,240 , −40 , 14 , −4 },   { 96 , 64 , −28 , −7 , 160 , −40 , 15 , −5 },  { 96 , 72 , 72 , −40 , 80 , −28 , 9 , −7 },   { 2 , 2 , 1 , 0 , −24 ,288 , −12 , −2 },   { −24 , 4 , 1 , −1 , 60 , 256 , −48 , 5 },   { −34 ,−12 , 1 , −2 , 160 , 192 , −48 , 3 },   { −24 , −2 , −12 , 1 , 224 , 96, −30 , −1 },   { −4 , −1 , 1 , 1 , 5 , −24 , 288 , −12 },   { 2 , −2 ,1 , −2 , −20 , 56 , 252 , −36 },   { 5 , −1 , 1 , −1 , −40 , 160 , 160 ,−33 },   { 2 , 0 , 4 , −4 , −36 , 224 , 80 , −18 },   { 2 , −4 , 0 , −1, −3 , 0 , −28 , 288 },   { −1 , −3 , −1 , −2 , 5 , −30 , 62 , 224 },  { −1 , 0 , 2 , −1 , 15 , −56 , 160 , 132 },   { −3 , 1 , 1 , −2 , 14 ,−56 , 240 , 56 },  },  {   { −80 , 48 , −6 , 0 , 256 , 63 , −40 , 12 },  1−192 , 160 , 28 , −10 , 224 , 80 , −48 , 12 },   { −192 , −10 , 224 ,−5 , 160 , 112 , −48 , 10 },   { −144 , 14 , −60 , 252 , 96 , 124 , −40, 9 },   { 10 , 1 , 3 , −1 , −80 , 248 , 112 , −40 },   { 3 , 6 , 4 , 1, −68 , 192 , 160 , −48 },   { −9 , 3 , 18 , −5 , −62 , 160 , 192 , −48},   { −20 , −4 , −15 , 36 , −60 , 132 , 224 , −48 },   { −3 , 2 , 1 , 1, 20 , −72 , 224 , 80 },   { −3 , 3 , −2 , −1 , 18 , −66 , 192 , 112 },  { −4 , 1 , −3 , −2 , 16 , −60 , 160 , 144 },   { −3 , 2 , 1 , 3 , 15 ,−48 , 120 , 160 },   { 0 , −3 , −1 , −2 , −12 , 24 , −72 , 320 },   { −3, 1 , −3 , −2 , −14 , 20 , −68 , 320 },   { 2 , 2 , 4 , 2 , −12 , 28 ,−64 , 288 },   { 1 , 0 , 2 , 5 , −14 , 24 , −56 , 288 },  },  {   { −72, −7 , −2 , 8 , 320 , 17 , −12 , 3 },   { −40 , −36 , −2 , 12 , 320 , 9, −9 , 2 },   { −48 , −7 , −28 , 17 , 320 , 5 , −6 , 2 },   { −56 , −10, −2 , 7 , 320 , 3 , −7 , 1 },   { 20 , −2 , −2 , 3 , −96 , 320 , 31 ,−17 },   { 10 , 1 , −4 , 5 , −80 , 320 , 20 , −15 },   { 14 , −9 , 0 , 8, −80 , 320 , 20 , −16 },   { 15 , −5 , −4 , 18 , −68 , 288 , 20 , −10},   { −8 , 1 , 1 , 5 , 31 , −96 , 288 , 31 },   { −10 , −1 , −1 , 7 ,28 , −80 , 288 , 24 },   { −9 , −4 , 0 , 12 , 28 , −80 , 288 , 20 },   {−10 , −7 , −4 , 15 , 24 , −72 , 288 , 20 },   { 1 , 0 , −2 , 2 , −14 ,28 , −80 , 320 },   { −3 , 0 , −2 , 7 , −10 , 24 , −80 , 320 },   { −4 ,−4 , −2 , 12 , −10 , 24 , −80 , 320 },   { −6 , −6 , −7 , 17 , −10 , 20, −72 , 320 },  },  {   { −96 , 20 , 10 , 6 , 224 , 264 , 72 , 24 },   {−28 , −24 , 14 , 12 , 80 , 320 , 112 , 36 },   { −15 , 18 , −15 , 6 , 32, 320 , 136 , 40 },   { −10 , 12 , 30 , −18 , 4 , 320 , 144 , 40 },   {12 , −4 , 2 , 2 , −14 , 272 , 224 , 28 },   { 4 , 10 , −2 , −4 , 7 , 224, 252 , 34 },   { −1 , 7 , 4 , −10 , 9 , 224 , 264 , 36 },   { −3 , 9 ,2 , −9 , 14 , 224 , 256 , 36 },   { 7 , 2 , 6 , −2 , 8 , 96 , 320 , 80},   { 5 , 7 , 2 , −4 , 7 , 112 , 320 , 80 },   { 2 , 14 , 2 , −8 , 6 ,124 , 320 , 72 },   { 2 , 15 , 8 , −8 , 10 , 136 , 288 , 80 },   { 5 , 0, 3 , −6 , 7 , 36 , 224 , 252 },   { 2 , 8 , 0 , −8 , 8 , 56 , 320 , 144},     { 4 , 14 , 5 , −7 , 12 , 72 , 320 , 112 },   { 1 , 12 , 3 , −8 ,14 , 80 , 320 , 112 },  },  {   { 96 , 80 , −12 , 1 , 12 , 80 , −2 , 2},   { −28 , 224 , 40 , −5 , −24 , 34 , 9 , 5 },   { −3 , −30 , 272 , 12, −24 , 14 , 9 , 8 },   { −7 , 12 , −72 , 320 , −12 , 0 , 3 , 2 },   {36 , 62 , −9 , −2 , −80 , 192 , 62 , −4 },   { −32 , 192 , 30 , −1 , −80, 80 , 48 , 18 },   { −10 , −10 , 256 , 1 , −48 , 18 , 17 , 28 },   { −7, 12 , −66 , 288 , −12 , −5 , −1 , 20 },   { 14 , 56 , −4 , 1 , −48 , 3, 160 , 72 },   { −48 , 160 , 28 , −2 , −80 , 28 , 72 , 96 },   { −24 ,3 , 240 , −4 , −72 , 20 , 3 , 80 },   { −16 , 6 , −60 , 288 , −30 , 4 ,−28 , 40 },   { 5 , 48 , −2 , 0 , −36 , 2 , −18 , 256 },   { −56 , 132 ,24 , −3 , −64 , 3 , −7 , 224 },   { −40 , 14 , 192 , 0 , −72 , 6 , −12 ,144 },   { −24 , 2 , −48 , 252 , −40 , −2 , −20 , 64 }  } };

Array 9. Exemplary values of MIP coefficients selected based on theproposed method, defined in C/C++ programming language.

   const short mipMatrix16x16round_const[6][64][8] = {  {   { −48 , 32 ,28 , 9 , 248 , −20 , 9 , −2 },   { −56 , 10 , 40 , 33 , 224 , 2 , 6 , −3},   { −28 , −28 , 48 , 66 , 160 , 36 , 3 , −1 },   { −9 , −33 , 34 , 96, 96 , 72 , −1 , 1 },   { −8 , −6 , −9 , 128 , 48 , 112 , −9 , 0 },   {−6 , 15 , −24 , 144 , 3 , 132 , −10 , 2 },   { 0 , 17 , −5 , 128 , −36 ,160 , −12 , 2 },   { 8 , 16 , 12 , 120 , −60 , 160 , −7 , 5 },   { −14 ,−17 , −1 , 24 , 112 , 160 , −12 , 2 },   { −6 , −16 , −12 , 36 , 72 ,192 , −12 , 3 },   { −7 , −8 , −24 , 40 , 40 , 224 , −12 , 2 },   { −6 ,−4 , −24 , 40 , 17 , 240 , −10 , 2 },   { −2 , −4 , −17 , 40 , 0 , 240 ,−4 , 2 },   { −1 , −3 , −12 , 40 , −16 , 240 , 4 , 2 },   { 0 , 2 , −12, 48 , −28 , 224 , 16 , 3 },   { −3 , 3 , −15 , 48 , −36 , 224 , 28 , 4},   { 1 , 0 , −12 , 14 , −5 , 252 , 2 , 5 },   { 2 , 0 , −14 , 17 , −12, 248 , 10 , 4 },   { 1 , −2 , −15 , 17 , −14 , 240 , 28 , 1 },   { 0 ,−3 , −14 , 17 , −15 , 224 , 48 , −2 },   { −1 , −2 , −14 , 17 , −14 ,192 , 80 , −5 },   { −3 , 0 , −12 , 18 , −14 , 160 , 112 , −7 },   { −3, 0 , −12 , 18 , −12 , 136 , 132 , −6 },   { −2 , 0 , −10 , 20 , −12 ,112 , 144 , 1 },   { 3 , 2 , −5 , 9 , −15 , 144 , 120 , −4 },   { −1 , 0, −7 , 7 , −14 , 120 , 160 , −9 },   { −1 , 0 , −8 , 8 , −9 , 80 , 192 ,−7 },   { 0 , 1 , −7 , 10 , −5 , 66 , 192 , −4 },   { −3 , −2 , −9 , 8 ,−5 , 40 , 224 , 0 },   { −3 , −1 , −10 , 9 , −4 , 28 , 224 , 10 },   {−4 , −2 , −10 , 10 , −5 , 16 , 224 , 24 },   { −1 , 1 , −8 , 15 , −3 ,16 , 192 , 40 },   { −1 , 0 , −4 , 4 , −3 , 10 , 240 , 9 },   { −1 , 0 ,−5 , 3 , −2 , −1 , 240 , 20 },   { −1 , −1 , −6 , 5 , −3 , −4 , 224 , 40},   { −1 , 0 , −6 , 8 , −3 , −4 , 192 , 66 },   { 0 , 0 , −6 , 9 , −3 ,−2 , 160 , 96 },   { −1 , 0 , −7 , 10 , −5 , −2 , 144 , 112 },   { −1 ,0 , −8 , 14 , −5 , 1 , 120 , 132 },   { 0 , 1 , −8 , 16 , −5 , 7 , 96 ,144 },   { −1 , 1 , −2 , 3 , −1 , −12 , 144 , 124 },   { −3 , 0 , −4 , 3, −3 , −10 , 112 , 160 },   { −3 , −1 , −6 , 5 , −6 , −6 , 80 , 192 },  { −1 , 0 , −4 , 8 , −4 , −2 , 64 , 192 },   { −2 , −1 , −7 , 9 , −7 ,−3 , 40 , 224 },   { −2 , 0 , −7 , 14 , −7 , 0 , 30 , 224 },   { −3 , −1, −9 , 14 , −9 , 0 , 20 , 240 },   { −3 , −1 , −9 , 15 , −10 , 2 , 17 ,240 },   { −1 , 0 , −2 , 3 , −1 , −2 , 5 , 252 },   { −2 , 0 , −3 , 5 ,−2 , −2 , −6 , 264 },   { −3 , −1 , −5 , 7 , −3 , −3 , −10 , 272 },   {−2 , 0 , −5 , 10 , −4 , −4 , −14 , 272 },   { −3 , 0 , −7 , 14 , −4 , −4, −16 , 272 },   { −3 , 1 , −8 , 17 , −5 , −5 , −17 , 272 },   { −3 , 1, −8 , 18 , −7 , −5 , −17 , 272 },   { −3 , 0 , −9 , 18 , −8 , −4 , −15, 272 },   { −1 , 0 , −2 , 6 , 1 , −5 , −34 , 288 },   { −1 , −1 , −2 ,7 , −1 , −5 , −32 , 288 },   { −2 , 0 , −4 , 10 , −2 , −7 , −31 , 288 },  { 0 , −1 , −5 , 12 , −3 , −8 , −31 , 288 },   { −2 , 0 , −6 , 15 , −4, −9 , −30 , 288 },   { −3 , 0 , −8 , 18 , −5 , −10 , −30 , 288 },   {−3 , 1 , −9 , 18 , −7 , −10 , −28 , 288 },   { −4 , 1 , −10 , 18 , −8 ,−12 , −24 , 288 }   }, //merge5  {   { 80 , 15 , 0 , −1 , 160 , 6 , −1 ,−3 },   { 120 , 34 , 2 , −1 , 96 , 9 , −1 , −3 },   { 112 , 72 , 9 , −1, 56 , 7 , 2 , −1 },   { 72 , 120 , 24 , −1 , 36 , 4 , 3 , −1 },   { 40, 120 , 72 , 0 , 24 , 1 , 2 , −3 },   { 28 , 62 , 136 , 12 , 14 , 1 , 4, 0 },   { 20 , 14 , 144 , 68 , 8 , 1 , 3 , −3 },   { 16 , 10 , 34 , 192, 6 , 1 , 0 , −2 },   { 20 , 6 , 2 , 1 , 160 , 66 , 1 , 0 },   { 48 , 12, 2 , 0 , 160 , 36 , 1 , −2 },   { 80 , 28 , 1 , 0 , 124 , 24 , 1 , −3},   { 96 , 48 , 5 , 0 , 96 , 14 , 2 , −4 },   { 96 , 80 , 18 , −1 , 62, 6 , 1 , −5 },   { 68 , 96 , 48 , 2 , 40 , 4 , 2 , −4 },   { 48 , 80 ,80 , 12 , 30 , 4 , 4 , −1 },   { 40 , 48 , 96 , 48 , 20 , 3 , 3 , −2 },  { 5 , 2 , 2 , 1 , 80 , 160 , 6 , −1 },   { 16 , 2 , 1 , 1 , 124 , 112, 4 , −4 },   { 36 , 8 , 1 , 1 , 136 , 72 , 4 , −2 },   { 60 , 20 , 1 ,1 , 128 , 48 , 3 , −4 },   { 80 , 36 , 3 , −1 , 112 , 31 , 1 , −5 },   {80 , 62 , 12 , 2 , 80 , 20 , 3 , −3 },   { 72 , 72 , 30 , 2 , 64 , 15 ,3 , −3 },   { 60 , 72 , 56 , 10 , 48 , 12 , 3 , −5 },   { 1 , −3 , −2 ,−1 , 17 , 192 , 60 , −7 },   { 5 , 0 , 1 , 2 , 56 , 160 , 34 , −3 },   {12 , 1 , −2 , 0 , 96 , 132 , 20 , −5 },   { 28 , 4 , −3 , −1 , 112 , 112, 9 , −6 },   { 48 , 15 , 0 , 0 , 112 , 80 , 6 , −5 },   { 60 , 30 , 1 ,0 , 112 , 56 , 3 , −6 },   { 64 , 48 , 9 , 1 , 96 , 40 , 3 , −5 },   {62 , 60 , 24 , 5 , 72 , 34 , 3 , −5 },   { 1 , −2 , 1 , 0 , 6 , 96 , 160, −7 },   { 1 , −2 , 0 , 1 , 24 , 128 , 112 , −6 },   { 3 , −2 , 0 , 1 ,48 , 144 , 68 , −5 },   { 10 , 0 , −1 , 1 , 68 , 136 , 48 , −6 },   { 20, 5 , 1 , 3 , 80 , 124 , 28 , −4 },   { 34 , 14 , 1 , 2 , 96 , 96 , 17 ,−5 },   { 40 , 28 , 3 , 3 , 96 , 80 , 12 , −5 },   { 48 , 40 , 10 , 5 ,80 , 68 , 10 , −5 },   { 2 , 1 , 3 , 2 , 7 , 14 , 192 , 36 },   { −3 ,−2 , −2 , −2 , 7 , 56 , 192 , 9 },   { −3 , −1 , 0 , 0 , 18 , 96 , 144 ,2 },   { 1 , −1 , 1 , 1 , 36 , 126 , 96 , −3 },   { 6 , −2 , 0 , 1 , 48, 136 , 72 , −5 },   { 15 , 2 , 0 , 2 , 68 , 128 , 48 , −7 },   { 24 ,10 , 0 , 3 , 72 , 120 , 34 , −6 },   { 32 , 20 , 4 , 3 , 80 , 96 , 28 ,−7 },   { 0 , −1 , −1 , −1 , 0 , 3 , 96 , 160 },   { −2 , −1 , −1 , −1 ,2 , 17 , 144 , 96 },   { −4 , −2 , −1 , 0 , 7 , 48 , 160 , 48 },   { −6, −3 , 1 , 2 , 18 , 80 , 144 , 18 },   { −3 , −3 , 2 , 2 , 30 , 96 , 126, 5 },   { 3 , −3 , 0 , 3 , 40 , 120 , 96 , −3 },   { 10 , 2 , −1 , 3 ,56 , 120 , 72 , −5 },   { 16 , 10 , 2 , 4 , 60 , 112 , 56 , −3 },   { 0, −2 , −1 , 0 , 0 , 14 , −28 , 272 },   { 0 , 0 , 1 , 2 , 3 , 20 , 36 ,192 },   { −4 , −2 , −1 , 1 , 2 , 28 , 96 , 136 },   { −5 , −3 , 0 , 1 ,8 , 48 , 128 , 80 },   { −5 , −4 , 1 , 2 , 15 , 64 , 136 , 48 },   { −2, −4 , 1 , 4 , 24 , 80 , 126 , 28 },   { 8 , 5 , 4 , 8 , 40 , 96 , 80 ,14 },   { 8 , 5 , 4 , 8 , 40 , 96 , 80 , 14 }   }, //merge10  {   { 72 ,16 , 6 , 4 , 136 , 10 , 8 , 4 },   { 48 , 80 , 4 , 9 , 68 , 33 , 10 , 4},   { −14 , 144 , 15 , 16 , 36 , 40 , 14 , 5 },   { −28 , 96 , 80 , 17, 18 , 48 , 18 , 7 },   { −17 , 24 , 144 , 34 , 2 , 40 , 20 , 8 },   {−10 , −5 , 96 , 112 , −7 , 36 , 28 , 9 },   { −10 , −3 , 20 , 192 , −14, 28 , 33 , 10 },   { −6 , −2 , −9 , 224 , −18 , 12 , 40 , 18 },   { −10, 18 , 8 , 5 , 112 , 120 , −4 , 8 },   { −12 , 40 , 16 , 17 , 56 , 120 ,9 , 12 },   { −24 , 60 , 24 , 28 , 14 , 120 , 20 , 14 },   { −24 , 40 ,48 , 40 , −10 , 112 , 34 , 17 },   { −18 , 12 , 64 , 64 , −28 , 96 , 48, 18 },   { −14 , −5 , 48 , 112 , −33 , 63 , 63 , 24 },   { −7 , −5 , 12, 144 , −33 , 40 , 72 , 33 },   { −3 , −5 , −2 , 160 , −32 , 18 , 72 ,48 },   { −8 , 9 , 10 , 12 , 12 , 192 , 10 , 18 },   { −10 , 15 , 15 ,24 , −4 , 160 , 36 , 20 },   { −14 , 14 , 16 , 40 , −20 , 136 , 62 , 24},   { −14 , 8 , 18 , 56 , −31 , 96 , 96 , 28 },   { −12 , 1 , 18 , 72 ,−36 , 66 , 112 , 36 },   { −9 , −3 , 12 , 96 , −40 , 40 , 112 , 48 },  { −5 , −4 , 3 , 112 , −36 , 18 , 96 , 72 },   { −3 , −5 , 1 , 120 ,−36 , 3 , 80 , 96 },   { −4 , −1 , 6 , 14 , −16 , 136 , 112 , 10 },   {−5 , −2 , 6 , 24 , −16 , 96 , 128 , 24 },   { −8 , −1 , 4 , 36 , −20 ,60 , 144 , 40 },   { −8 , −1 , 2 , 48 , −24 , 36 , 144 , 60 },   { −5 ,−2 , 4 , 60 , −28 , 20 , 128 , 80 },   { −5 , −3 , −2 , 68 , −31 , 6 ,112 , 112 },   { −3 , −3 , −1 , 80 , −30 , −4 , 80 , 136 },   { −3 , −5, −2 , 80 , −31 , −10 , 66 , 160 },   { 0 , −2 , 2 , 16 , −7 , 24 , 192, 30 },   { 0 , −3 , 1 , 28 , −10 , 16 , 160 , 63 },   { −4 , −2 , −5 ,34 , −15 , 7 , 144 , 96 },   { −3 , −1 , −6 , 40 , −18 , 2 , 112 , 128},   { −2 , −2 , −4 , 48 , −20 , −4 , 80 , 160 },   { −3 , −3 , −6 , 48, −24 , −10 , 63 , 192 },   { 0 , −1 , −4 , 56 , −24 , −12 , 48 , 192 },  { 2 , 0 , −1 , 60 , −24 , −12 , 36 , 192 },   { 0 , −5 , −4 , 12 , −6, −5 , 144 , 120 },   { −1 , −5 , −9 , 20 , −12 , −8 , 112 , 160 },   {−2 , −1 , −12 , 28 , −14 , −9 , 72 , 192 },   { 0 , 1 , −8 , 34 , −12 ,−9 , 56 , 192 },   { −1 , −1 , −6 , 34 , −17 , −14 , 34 , 224 },   { −1, −2 , −6 , 36 , −20 , −15 , 20 , 240 },   { 1 , −1 , −4 , 40 , −20 ,−17 , 14 , 240 },   { 1 , −2 , −2 , 40 , −20 , −18 , 7 , 248 },   { 1 ,−3 , −6 , 10 , −4 , −6 , 40 , 224 },   { 1 , −1 , −12 , 18 , −7 , −9 ,24 , 240 },   { −1 , 2 , −14 , 24 , −8 , −12 , 12 , 252 },     { −2 , 2, −12 , 24 , −10 , −16 , 4 , 264 },   { 0 , 0 , −5 , 24 , −12 , −16 , −2, 264 },   { 0 , −1 , −3 , 24 , −14 , −18 , −9 , 272 },   { 1 , −1 , −2, 28 , −15 , −20 , −12 , 272 },   { 1 , −1 , −2 , 31 , −18 , −20 , −14 ,272 },   { 2 , −1 , −8 , 9 , −2 , −6 , −12 , 272 },   { 3 , 1 , −10 , 15, −3 , −10 , −14 , 272 },   { −1 , 2 , −12 , 15 , −7 , −15 , −18 , 288},   { −3 , 3 , −10 , 17 , −7 , −16 , −20 , 288 },   { −1 , 1 , −5 , 17, −8 , −17 , −24 , 288 },   { −1 , 0 , −3 , 18 , −9 , −20 , −24 , 288 },  { −1 , 0 , −2 , 20 , −12 , −20 , −24 , 288 },   { 0 , −2 , −3 , 24 ,−14 , −20 , −24 , 288 }   }, //merge5  {   { −20 , 96 , −14 , −4 , 192 ,14 , −6 , −1 },   { −40 , 160 , 12 , −5 , 68 , 80 , −20 , 2 },   { −17 ,80 , 96 , −4 , 5 , 112 , −14 , −2 },   { 2 , −3 , 160 , 24 , −15 , 80 ,18 , −10 },   { 6 , −12 , 96 , 96 , −10 , 40 , 48 , −7 },   { 4 , −2 ,24 , 160 , −9 , 12 , 62 , 5 },   { 1 , 0 , −1 , 192 , −7 , −12 , 56 , 28},   { 5 , 4 , 2 , 160 , −5 , −20 , 48 , 60 },   { −30 , 48 , 24 , −3 ,56 , 192 , −40 , 8 },   { −4 , 8 , 72 , 4 , −7 , 192 , −6 , −3 },   { 5, −17 , 80 , 40 , −20 , 120 , 56 , −7 },   { 5 , −14 , 40 , 96 , −16 ,48 , 96 , 3 },   { 5 , −6 , 10 , 124 , −10 , 6 , 96 , 32 },   { 5 , 0 ,−6 , 136 , −9 , −15 , 80 , 64 },   { 3 , 5 , −10 , 132 , −9 , −24 , 64 ,96 },   { 6 , 6 , −5 , 120 , −10 , −28 , 40 , 126 },   { 7 , −10 , 33 ,5 , −24 , 224 , 24 , −3 },   { 8 , −20 , 34 , 34 , −18 , 112 , 112 , −6},   { 6 , −14 , 10 , 68 , −10 , 34 , 144 , 18 },   { 4 , −5 , −9 , 96 ,−9 , −4 , 124 , 60 },   { 3 , 1 , −12 , 96 , −7 , −17 , 96 , 96 },   { 3, 4 , −12 , 96 , −8 , −24 , 66 , 132 },   { 5 , 6 , −6 , 80 , −8 , −24 ,40 , 160 },   { 5 , 8 , 0 , 80 , −8 , −20 , 28 , 160 },   { 7 , −15 , 10, 20 , −14 , 68 , 192 , −12 },   { 2 , −12 , −6 , 48 , −6 , 9 , 192 , 30},   { 4 , −2 , −12 , 63 , −1 , −7 , 132 , 80 },   { 4 , 1 , −15 , 66 ,−3 , −14 , 80 , 136 },   { 4 , 4 , −12 , 64 , −4 , −16 , 56 , 160 },   {1 , 4 , −8 , 60 , −7 , −18 , 30 , 192 },   { 3 , 7 , −2 , 56 , −6 , −17, 18 , 192 },   { 4 , 6 , 2 , 56 , −6 , −16 , 14 , 192 },   { 3 , −5 ,−8 , 28 , 0 , −3 , 192 , 48 },   { 2 , −2 , −16 , 40 , −2 , −10 , 124 ,120 },   { 1 , 2 , −17 , 48 , −1 , −10 , 72 , 160 },   { 3 , 3 , −14 ,48 , −3 , −12 , 36 , 192 },   { 1 , 1 , −10 , 40 , −7 , −12 , 17 , 224},   { 3 , 3 , −6 , 40 , −8 , −12 , 9 , 224 },   { 2 , 5 , −2 , 40 , −9, −12 , 4 , 224 },   { 2 , 4 , −1 , 40 , −9 , −12 , 3 , 224 },   { 1 , 0, −14 , 20 , −1 , −5 , 96 , 160 },   { 3 , 2 , −15 , 30 , −2 , −3 , 48 ,192 },   { 1 , 2 , −16 , 31 , −3 , −5 , 20 , 224 },   { 0 , 1 , −12 , 30, −6 , −8 , 7 , 240 },   { 1 , 2 , −7 , 30 , −7 , −8 , 2 , 240 },   { 1, 2 , −4 , 28 , −8 , −8 , −1 , 240 },   { 1 , 3 , −2 , 28 , −9 , −9 , −2, 240 },   { 1 , 3 , 0 , 28 , −10 , −9 , −3 , 240 },   { −1 , 1 , −14 ,14 , −3 , −2 , 20 , 240 },   { 0 , 3 , −14 , 18 , −3 , −2 , 4 , 248 },  { 0 , 3 , −12 , 20 , −5 , −3 , −1 , 252 },   { 0 , 1 , −8 , 20 , −6 ,−5 , −3 , 252 },   { 1 , 1 , −4 , 18 , −8 , −6 , −3 , 252 },   { 1 , 1 ,−2 , 18 , −10 , −6 , −4 , 252 },   { 0 , 2 , 0 , 20 , −10 , −7 , −5 ,248 },   { 1 , 2 , 1 , 20 , −10 , −7 , −1 , 240 },   { 0 , 3 , −12 , 8 ,−1 , −1 , −1 , 256 },   { 0 , 3 , −12 , 12 , −4 , −1 , −3 , 256 },   { 0, 3 , −9 , 12 , −5 , −2 , 0 , 252 },   { 0 , 2 , −5 , 12 , −6 , −4 , −1, 252 },   { 0 , 1 , −3 , 12 , −7 , −5 , −1 , 252 },   { 0 , 2 , −1 , 14, −9 , −5 , −1 , 248 },   { −1 , 2 , 0 , 15 , −9 , −5 , −3 , 248 },   {1 , 1 , 1 , 17 , −9 , −5 , −2 , 240 }   }, //merge5  {   { −36 , 15 , 1, 0 , 320 , −48 , 6 , −1 },   { −34 , 17 , 6 , 6 , 288 , −40 , 10 , 2 },  { −33 , 15 , 8 , 6 , 288 , −40 , 10 , 2 },   { −36 , 15 , 10 , 6 , 288, −40 , 9 , 2 },   { −40 , 20 , 7 , 9 , 288 , −40 , 9 , 2 },   { −48 ,20 , 12 , 10 , 288 , −36 , 8 , 1 },   { −56 , 14 , 31 , 7 , 288 , −36 ,7 , 1 },   { −60 , 9 , 28 , 28 , 272 , −31 , 7 , 2 },   { −40 , 1 , −1 ,−1 , 224 , 96 , −24 , 2 },   { −40 , 1 , −2 , −1 , 224 , 96 , −24 , 2 },  { −48 , 7 , −2 , 1 , 224 , 96 , −24 , 3 },   { −48 , 6 , −1 , 1 , 224, 96 , −24 , 2 },   { −40 , −1 , 2 , −2 , 224 , 96 , −24 , 1 },   { −40, −2 , 1 , 0 , 224 , 96 , −24 , 0 },   { −40 , 3 , 1 , 8 , 192 , 112 ,−24 , 4 },   { −40 , 3 , 1 , 7 , 192 , 112 , −24 , 4 },   { −1 , −2 , −1, −2 , 7 , 288 , −36 , 2 },   { −1 , −2 , −1 , −1 , 7 , 288 , −36 , 3 },  { −2 , −1 , 0 , −1 , 6 , 288 , −36 , 2 },   { −2 , −2 , 1 , 0 , 6 ,288 , −36 , 2 },   { −2 , −3 , 1 , 0 , 6 , 288 , −36 , 2 },   { −3 , −3, 0 , 0 , 6 , 288 , −34 , 2 },   { −4 , −5 , 0 , 1 , 7 , 288 , −33 , 1},   { −5 , −3 , 2 , 4 , 10 , 272 , −28 , 3 },   { 12 , −2 , 1 , 1 , −40, 192 , 112 , −20 },   { 10 , −1 , 2 , 2 , −40 , 192 , 112 , −20 },   {9 , 0 , 1 , 1 , −40 , 192 , 112 , −20 },   { 9 , 0 , 2 , 2 , −40 , 192 ,112 , −20 },   { 7 , −3 , 3 , 1 , −36 , 192 , 112 , −20 },   { 7 , −3 ,2 , 2 , −40 , 192 , 120 , −24 },   { 7 , −3 , 0 , 0 , −36 , 192 , 120 ,−24 },   { 6 , −4 , 1 , 1 , −36 , 192 , 120 , −24 },   { 3 , 0 , 1 , 1 ,−3 , 9 , 272 , −28 },   { 2 , 1 , 1 , 1 , −3 , 9 , 272 , −28 },   { 0 ,1 , 1 , 1 , −3 , 7 , 272 , −24 },   { 0 , 1 , 2 , 1 , −2 , 7 , 272 , −24},   { −1 , 1 , 2 , 2 , −3 , 7 , 272 , −24 },   { −1 , 0 , 2 , 2 , −3 ,7 , 272 , −24 },   { −1 , −1 , 1 , 2 , −4 , 7 , 272 , −20 },   { −1 , −1, 2 , 3 , −3 , 10 , 264 , −17 },   { 2 , 1 , 3 , 3 , 9 , −36 , 192 , 80},   { 1 , 3 , 3 , 3 , 10 , −36 , 192 , 80 },   { 0 , 3 , 3 , 3 , 9 ,−34 , 192 , 80 },   { 0 , 3 , 3 , 3 , 9 , −34 , 192 , 80 },   { 0 , 2 ,4 , 3 , 9 , −33 , 192 , 80 },   { −2 , 0 , 2 , 0 , 5 , −36 , 192 , 96 },  { −3 , 0 , 1 , 2 , 5 , −36 , 192 , 96 },   { −3 , −1 , 1 , 1 , 4 , −34, 192 , 96 },   { 0 , 0 , 0 , 1 , 2 , −3 , 16 , 240 },   { 0 , 0 , 0 ,−1 , 0 , −4 , 14 , 248 },   { −1 , 1 , 0 , −1 , 1 , −5 , 12 , 248 },   {−2 , 1 , 1 , −1 , 1 , −5 , 12 , 248 },   { −2 , 0 , 2 , −1 , 1 , −5 , 12, 248 },   { −2 , 0 , 2 , 0 , 0 , −5 , 12 , 248 },   { −2 , 0 , 2 , 1 ,1 , −6 , 12 , 248 },   { −3 , 0 , 2 , 2 , 2 , −3 , 16 , 240 },   { 1 ,−1 , −2 , −1 , −3 , 9 , −68 , 320 },   { −2 , 0 , −1 , −1 , −4 , 7 , −64, 320 },   { −2 , 1 , −1 , −1 , −3 , 8 , −66 , 320 },   { −3 , 1 , 0 ,−1 , −3 , 8 , −66 , 320 },   { −3 , 0 , 1 , −1 , −4 , 8 , −66 , 320 },  { −3 , −1 , 1 , −1 , −4 , 7 , −64 , 320 },   { −5 , −2 , 0 , 1 , −4 ,7 , −62 , 320 },   { −5 , −2 , 0 , 1 , −4 , 7 , −62 , 320 }   }, //merge10  {   { 60 , 20 , 8 , 2 , 160 , 1 , 3 , 2 },   { 16 , 96 , 5 , 3, 126 , 7 , 2 , 1 },   { −60 , 192 , 15 , 4 , 96 , 9 , 0 , −1 },   { −80, 160 , 96 , −4 , 80 , 9 , −3 , −3 },   { −72 , 60 , 192 , 6 , 62 , 10 ,−1 , −1 },   { −56 , 9 , 160 , 80 , 48 , 12 , 0 , 2 },   { −48 , 10 , 48, 192 , 40 , 12 , 0 , 1 },   { −48 , 15 , −24 , 264 , 32 , 14 , 0 , 2 },  { −36 , 36 , 6 , 2 , 160 , 96 , −10 , 1 },   { −80 , 96 , 12 , 4 , 160, 72 , −6 , −3 },   { −136 , 144 , 28 , 8 , 144 , 72 , −2 , −1 },   {−160 , 144 , 80 , 8 , 128 , 62 , −4 , −3 },   { −160 , 72 , 144 , 24 ,112 , 60 , 1 , 1 },   { −136 , 32 , 132 , 80 , 96 , 56 , −2 , −2 },   {−126 , 20 , 48 , 192 , 80 , 48 , −2 , −4 },   { −112 , 20 , −4 , 240 ,64 , 48 , 0 , 0 },   { −32 , 28 , 8 , 4 , 34 , 224 , −12 , 2 },   { −80, 63 , 14 , 4 , 48 , 224 , −14 , −4 },   { −124 , 96 , 32 , 12 , 56 ,192 , −7 , −1 },   { −160 , 96 , 72 , 24 , 64 , 160 , −2 , 2 },   { −160, 62 , 112 , 32 , 62 , 160 , −8 , −5 },   { −160 , 36 , 96 , 80 , 66 ,144 , −2 , −3 },   { −160 , 28 , 48 , 160 , 66 , 120 , 0 , −4 },   {−160 , 28 , 9 , 192 , 63 , 112 , 9 , 2 },   { −24 , 20 , 10 , 6 , −20 ,192 , 80 , −7 },   { −63 , 40 , 15 , 8 , −20 , 224 , 60 , −9 },   { −96, 64 , 28 , 14 , −18 , 224 , 48 , −9 },   { −128 , 63 , 56 , 24 , −14 ,224 , 40 , −8 },   { −144 , 40 , 80 , 40 , −9 , 224 , 34 , −10 },   {−160 , 32 , 80 , 80 , 1 , 192 , 33 , −2 },   { −160 , 24 , 36 , 136 , 3, 192 , 28 , −3 },   { −160 , 20 , 10 , 192 , 6 , 160 , 28 , −2 },   {−24 , 15 , 8 , 4 , −5 , 48 , 224 , −14 },   { −48 , 33 , 16 , 12 , −6 ,72 , 192 , −14 },   { −80 , 40 , 24 , 16 , −15 , 96 , 192 , −17 },   {−96 , 40 , 40 , 28 , −16 , 112 , 160 , −12 },   { −120 , 28 , 60 , 48 ,−20 , 128 , 144 , −12 },   { −128 , 20 , 48 , 80 , −20 , 136 , 128 , −9},   { −136 , 17 , 28 , 120 , −24 , 144 , 112 , −6 },   { −144 , 16 , 9, 160 , −24 , 144 , 96 , −1 },   { −20 , 10 , 7 , 4 , 3 , −28 , 224 , 56},   { −48 , 20 , 10 , 12 , 2 , −20 , 240 , 40 },   { −66 , 28 , 18 , 20, −2 , −10 , 240 , 28 },   { −80 , 24 , 32 , 31 , −4 , 4 , 224 , 24 },  { −96 , 15 , 40 , 48 , −9 , 17 , 224 , 17 },   { −112 , 10 , 33 , 72 ,−14 , 30 , 224 , 12 },   { −112 , 8 , 15 , 112 , −18 , 48 , 192 , 10 },  { −124 , 7 , 3 , 132 , −24 , 56 , 192 , 12 },   { −12 , 9 , 7 , 5 , −1, −6 , 62 , 192 },   { −32 , 14 , 6 , 10 , −5 , −10 , 80 , 192 },   {−48 , 18 , 15 , 24 , −3 , −8 , 96 , 160 },   { −60 , 10 , 24 , 31 , −5 ,−7 , 120 , 144 },   { −72 , 4 , 28 , 48 , −9 , −7 , 136 , 128 },   { −80, 3 , 18 , 72 , −12 , −3 , 144 , 112 },   { −96 , 3 , 7 , 96 , −12 , 0 ,160 , 96 },   { −96 , 2 , −4 , 112 , −18 , 4 , 160 , 96 },   { −14 , 4 ,2 , 4 , −7 , 14 , −68 , 320 },   { −24 , 12 , 6 , 16 , −3 , 17 , −56 ,288 },   { −36 , 9 , 8 , 20 , −6 , 12 , −40 , 288 },   { −48 , 4 , 14 ,34 , −8 , 12 , −24 , 272 },   { −56 , −2 , 14 , 48 , −12 , 10 , −12 ,264 },   { −66 , −2 , 7 , 66 , −12 , 9 , 5 , 248 },   { −80 , −3 , −8 ,96 , −16 , 9 , 32 , 224 },   { −80 , −3 , −8 , 96 , −16 , 9 , 32 , 224 } } //merge10 };

The modified signaling is represented in Table 11.

TABLE 11 Unified signaling for directional and MIP modes   ...  if(treeType = = SINGLE_TREE || treeType = =  DUAL_TREE_LUMA ) }    if( Abs(Log2( cbWidth ) - Log2( cbHeight ) ) <= 2)     intra_lwip_flag[ x0 ][ y0] ae(v)    if( !intra_lwip_flag[ x0 ][ y0 ] ) }     if( ( y0 % CtbSizeY) > 0)      intra_luma_ref_idx[ x0 ][ y0 ] ae(v)     if(intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&      ( cbWidth <= MaxTbSizeY ||cbHeight <= MaxTbSizeY ) &&      ( cbWidth * cbHeight > MinTbSizeY *MinTbSizeY ))      intra_subpartitions_mode_flag[ x0 ][ y0 ] ae(v)    if( intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&      cbWidth<= MaxTbSizeY && cbHeight <= MaxTbSizeY )     intra_subpartitions_split_flag[ x0 ][ y0 ] ae(v)    }     if(intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&     intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0)     intra_luma_mpm_flag[ x0 ][ y0 ] ae(v)     if( intra_luma_mpm_flag[x0 ][ y0 ] ) }      if( intra_lwip_flag[ x0 ][ y0 ] )      intra_lwip_mpm_idx[ x0 ][ y0 ]      else       intra_luma_mpm_idx[x0 ][ y0 ] ae(v)     }     else {      if( intra_lwip_flag[ x0 ][ y0 ] )      intra_lwip_mpm_remainder[ x0 ][ y0 ] ae(v)      else      intra_luma_mpm_remainder[ x0 ][ y0 ]     } ...

If infra_lwip_flag is not signaled, it is inferred to 0.

Derivation of the MPM list in the case of joint signaling is representedas follows:

MPM coding (intra_luma_mpm_idx) is not modified, i.e. the process fordirectional intra prediction mode is invoked.

Non-MPM coding (intra_luma_mpm_remainder) is invoked. For the case whenintra_lwip_flag is 1, this symbol is encoded using a truncated unarycode, or a fixed-length code, depending on the value ofintra_lwip_mpm_flag. When this flag is set equal to 0, the number of themodes coded by this fixed-length code is set as follows.

-   -   cMax=(cbWidth==4 && cbHeight==4)?    -   31:((cbWidth<=8 && cbHeight<=8)?15:7)

When intra_lwip_mpm_flag is equal to 1 the number of the modes thatcould be encoded using truncated unary code is fixed and does not dependon the dimensions of the current block.

Another embodiment of the present disclosure facilitates the usage of aspecial flag for MPM coding. This flag may be referred to asintra_luma_planar_flag or intra_luma_not_planar_flag, indicating intraprediction mode being or not being planar, respectively. When mpm_flagis equal to zero, intra_luma_planar_flag is not signaled. In accordancewith the embodiment, the unified signaling mechanism could be defined asfollows (see Table 12). In this embodiment MIP MPM signaling is enabledonly for the case when intra_luma_not_planar_flag is set equal to 0 thusindicating that intra prediction mode is non-planar. Otherwise, whenintra_luma_not_planar_flag is set equal to 1, it is indicated that intraprediction mode is planar. In this case no additional MIP-relatedsignaling is required since is known that planar mode does not belong tothe set of MIP modes.

TABLE 12 Unified signaling for directional and MIP modes facilitatingintra_luma_non_planar_flag       ...  if( treeType = = SINGLE_TREE ||treeType = = DUAL_TREE_LUMA ) {   if( ( y0 % CtbSizeY ) > 0)   intra_luma_ref_idx[ x0 ][ y0 ]   if (intra_luma_ref_idx[ x0 ][ y0 ] == 0 &&    ( cbWidth <= MaxTbSizeY || cbHeight <= MaxTbSizeY ) &&    (cbWidth * cbHeight > MinTbSizeY * MinTbSizeY ))   intra_subpartitions_mode_flag[ x0 ][ y0 ]   if(intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&    cbWidth <=MaxTbSizeY && cbHeight <= MaxTbSizeY )   intra_subpartitions_split_flag[ x0 ][ y0 ]   if( intra_luma_ref_idx[x0 ][ y0 ] = = 0 &&    intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0)   intra_luma_mpm_flag[ x0 ][ y0 ]   if( intra_luma_mpm_flag[ x0 ][ y0 ]) {    if( intra_luma_ref_idx[ x0 ][ y0 ] = = 0)    intra_luma_not_planar_flag[ x0 ][ y0 ]    if(intra_luma_not_planar_flag[ x0 ][ y0 ] ) {     if (intra_luma_ref_idx[x0 ][ y0 ] = = 0 &&     intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0){      intra_lwip_flag[ x0 ][ y0 ]     }     if( intra_lwip_flag[ x0 ][y0 ] ) {      intra_lwip_mpm_idx[ x0 ][ y0 ]     } else     intra_luma_mpm_idx[ x0 ][ y0 ]    }   } else   {   intra_lwip_flag[ x0 ][ y0 ]    if(intra_lwip_flag[ x0 ][ y0 ] )    intra_lwip_mpm_remainder[ x0 ][ y0 ]   }

In another embodiment a more general intra_luma_head_mpm_flag is usedinstead of intra_luma_nonplanar_flag. As in the previous embodiment, itis assumed that among the set of casual intra prediction modes the mostprobable one is the planar mode. Therefore, when infra_lwip_flag is setto zero, intra_luma_head_mpm_flag being set to 1 indicates that intraprediction mode is planar. When infra_lwip_flag is set to 1,intra_luma_head_mpm_flag being set to 1 indicates that intra predictionmode is the most probable MIP mode. Table 13 gives the syntax of MIP,the MIP list part of which is based on intra_luma_head_mpm_flagsignaling.

TABLE 13 Unified signaling for directional and MIP modes facilitatingintra_luma_head_mpm_flag ...  if( treeType = = SINGLE_TREE || treeType == DUAL_TREE_LUMA_) {   if( ( y0 % CtbSizeY ) > 0)    intra_luma_ref idx[x0 ][ y0 ]   if (intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&    ( cbWidth <=MaxTbSizeY || cbHeight <= MaxTbSizeY ) &&    ( cbWidth * cbHeight >MinTbSizeY * MinTbSizeY ))    intra_subpartitions_mode_flag[ x0 ][ y0 ]  if( intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&    cbWidth <=MaxTbSizeY && cbHeight <= MaxTbSizeY )   intra_subpartitions_split_flag[ x0 ][ y0 ]   if( intra_luma_ref_idx[x0 ][ y0 ] = = 0 &&    intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0)   intra_luma_mpm_flag[ x0 ][ y0 ]   if( intra_luma_mpm_flag[ x0 ][ y0 ]) {    if( intra_luma_ref_idx[ x0 ][ y0 ] = = 0)    intra_luma_head_mpm_flag [ x0 ][ y0 ]     if (intra_luma_ref_idx[ x0][ y0 ] = = 0 &&     intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0) {     intra_lwip_flag[ x0 ][ y0 ]    }    if( intra_luma_head_mpm_flag [x0 ][ y0 ] = = 0) {     if( intra_lwip_flag[ x0 ][ y0 ] ) {     intra_lwip_mpm_idx[ x0 ][ y0 ]     } else      intra_luma_mpm_idx[x0 ][ y0 ]    }   } else   {    intra_lwip_flag[ x0 ][ y0 ]   if(intra_lwip_flag[ x0 ][ y0 ] )     intra_lwip_mpm_remainder[ x0 ][y0 ]   }

The most probable MIP modes' numbers are 17, 0 and 1 for the values ofMIP block size types 0, 1 and 2 respectively.

The MIP modes are defined by the multiplication matrices A and offsetmatrices b that are used in obtaining reduced predicted samplespred_(red) from the reduced boundary bdry_(red):

pred_(red) =A·bdry_(red) +b.

Multiplication matrix A and offset values b for the most probable mode17 of the MIP block size type 0 are given in table 14. Offset values bfor MIP block size types 1 and 2 are equal to 0. Multiplication matrix Afor the best mode 0 and MIP block size type 1 is given in Table 15.Multiplication matrix A for the best mode 1 and MIP block size type 2 isgiven in Table 16.

TABLE 14 Multiplication matrix A and offset values b for the mostprobable MIP mode 17 of block size type 0. block size type 0 matrix Abias −23 −3 283 −2 1 −18 −11 287 −2 1 −2 −26 287 −3 1 −1 −21 282 −4 1 182 234 3 −1 16 5 233 3 −1 13 7 231 5 −1 17 0 229 10 −1 2 −1 9 246 0 2 −16 249 0 1 1 3 251 0 −1 3 3 251 0 0 0 −11 267 0 0 1 −11 266 0 1 1 −10 2640 1 1 −9 263 0 (In Table 14 Multiplication matrix A is given in 8-bitprecision, i.e. the multiplication result A·bdry_(red) should beright-shifted by 8. Precision of multiplication matrices A in Table 15and Table 16 is 9 bits.)

TABLE 15 Multiplication matrix A for the most probable MIP mode 0 ofblock size type 1. block size type 1 matrix A 42 −26 8 −1 270 −41 7 −3192 −31 −4 1 131 −41 12 −4 128 146 −21 −3 10 −5 2 −2 14 136 111 1 −9 7−3 −1 −11 2 −2 1 35 267 −42 5 −34 0 2 1 197 126 −42 6 52 −41 8 1 257 −15−3 −1 132 15 −18 5 156 −40 11 −4 3 −1 0 1 −16 32 272 −36 9 −2 −1 1 −47199 129 −32 −13 6 −3 2 12 268 −11 −4 −15 −6 3 3 137 167 −35 3 −3 0 −2 14 −15 24 246 −5 0 −3 2 15 −56 202 101 1 −1 −3 2 −8 6 267 −9 5 0 −3 4 −29145 152 −18

TABLE 16 Multiplication matrix A for the most probable MIP mode 1 ofblock size type 2. block size type 2 matrix A 78 15 0 0 158 7 0 −2 11735 2 −1 96 9 0 −2 115 72 9 −1 55 7 1 −2 75 116 26 −1 36 4 3 −2 41 117 710 24 2 3 −2 28 62 138 12 14 1 3 −1 22 14 140 69 8 1 3 −2 16 10 34 188 72 1 −1 18 5 1 0 171 64 −1 −2 51 11 2 0 158 37 1 −3 81 28 1 0 123 24 1 −396 51 5 1 89 15 3 −3 89 78 19 0 63 8 3 −3 69 94 44 2 43 4 3 −3 51 78 8610 29 3 3 −3 38 49 98 47 21 3 3 −3 5 1 1 0 83 162 5 −2 16 2 1 1 123 1124 −3 37 8 1 1 135 74 3 −3 60 19 1 1 127 49 3 −4 77 38 4 0 107 32 2 −3 8061 11 1 84 21 2 −4 72 76 30 2 63 14 2 −4 59 72 55 11 48 12 3 −4 3 −1 0 119 178 61 −4 5 −1 0 1 55 166 33 −4 13 1 −1 1 90 134 20 −4 28 6 −1 1 109105 11 −4 45 15 0 1 114 78 7 −4 59 31 2 1 107 57 4 −5 64 49 9 1 92 43 3−5 62 59 23 5 74 34 3 −5 1 −2 1 0 7 87 167 −6 1 −2 0 1 22 129 112 −6 3−2 0 1 45 145 70 −5 10 0 −1 1 68 140 44 −6 21 4 0 1 87 123 27 −6 33 13 01 96 103 16 −7 44 27 2 2 94 83 11 −6 48 38 10 4 85 67 10 −6 0 −1 1 0 511 205 36 −2 −1 0 0 9 55 183 11 −3 −1 0 0 19 98 142 1 0 −2 0 0 35 125103 −4 6 −2 0 1 51 134 72 −6 15 2 0 2 66 129 49 −7 25 11 0 3 75 116 34−7 32 21 4 4 76 98 27 −6 0 −1 0 0 1 4 91 161 −2 −1 −1 0 3 18 146 91 −4−2 −1 1 8 46 164 44 −6 −3 0 1 17 77 151 17 −3 −4 1 1 29 102 125 4 3 −3 03 41 116 98 −2 10 2 0 4 52 119 74 −4 16 10 3 5 59 109 57 −2 0 −2 −1 0 114 −26 269 −2 −2 −1 0 1 17 33 208 −4 −2 −1 1 3 27 93 139 −5 −3 0 1 9 44129 82 −5 −4 1 2 16 65 135 47 −2 −4 1 3 25 83 125 26 2 −2 1 4 35 94 10615 7 3 2 6 42 96 87 12

When intra_luma_head_mpm_flag is signaled for MIP modes, the mostprobable MIP mode is indicated. This requires, that MPM list for MIPshould be constructed in such a manner that the first element of the MPMlist is always assigned to the same most probable MIP mode (e.g. 17, 0or 1 for the MIP block size type 0, 1 and 2, respectively).

The order of signaling MRLP index (intra_luma_ref_idx), ISP flag(intra_subpartitions_split_flag) and MIP flag (intra_lwip_flag) may bedifferent. Table 17 shows the embodiment of Table 10 wherein MRLP index(intra_luma_ref_idx) and ISP flag (intra_subpartitions_split_flag)follows MIP flag (intra_lwip_flag).

TABLE 17 Unified signaling for directional and MIP modes facilitatingintra_luma_non_planar_flag with alternative flag coding order.       ...  if( treeType = = SINGLE TREE || treeType = = DUALTREE_luma_) {    intra_luma_mpm_flag[ x0 ][ y0 ]   if(intra_luma_mpm_flag[ x0 ][ y0 ] ) {     intra_luma_not_planar_flag[ x0][ y0 ]    if( intra_luma_not_planar_flag[ x0 ][ y0 ] ) {     intra_lwip_flag[ x0 ][ y0 ]     if( intra_lwip_flag[ x0 ][ y0 ] ) {     intra_lwip_mpm_idx[ x0 ][ y0 ]     } else      intra_luma_mpm_idx[x0 ][ y0 ]    }   } else   {    intra_lwip_flag[ x0 ][ y0 ]   if(intra_lwip_flag[ x0 ][ y0 ] )     intra_lwip_mpm_remainder [ x0 ][y0 ]   }   if( intra_luma_mpm_flag == 1 && intra_luma_not_planar_flag ==  1 && (y0 % CtbSizeY ) > 0)    intra_luma_ref_idx[ x0 ][ y0 ]   if(intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&       ( cbWidth <= MaxTbSizeY|| cbHeight <= MaxTbSizeY )   &&       ( cbWidth * cbHeight >MinTbSizeY * MinTbSizeY ) &&   intra_lwip_flag == 0 &&intra_luma_mpm_flag == 1)    intra_subpartitions_mode_flag[ x0 ][ y0 ]  if( intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 &&       cbWidth<= MaxTbSizeY && cbHeight <=   MaxTbSizeY )   intra_subpartitions_split_flag[ x0 ][ y0 ]

FIG. 13 illustrates a method of intra prediction based on the presentdisclosure, wherein the method of the intra prediction is either adirectional intra prediction method or an ALWIP method, wherein themethod comprises the following steps. The step are preparing a set ofreference samples (step 1601); in case the method of intra predictionfor a first block is directional intra prediction (step 1603: yes),obtaining (step 1605) a first predicted signal of the first block of afirst picture by convolving the set of reference samples with a firstset of coefficients; obtaining (step 1607) a first reconstructed blockof the first picture based on the first predicted signal; and in casethe method of intra prediction of a second block is ALWIP (step 1603:no), obtaining (step 1609) a second predicted signal of the second blockof a second picture by convolving the set of reference samples with asecond set of coefficients, wherein the second set of coefficientscomprises coefficients of a core matrix A of ALWIP, and the coefficientsof the core matrix A and the first set of coefficients have sameprecision; upsampling (1611) the second predicted signal; and obtaining(1613) a second reconstructed block of the second picture based on theupsampled second predicted signal.

FIG. 14 illustrates an encoder 20 based on the present disclosure. Theencoder 20 of FIG. 14 comprises a preparing unit 2001 configured toprepare a set of reference samples; a first obtaining unit 2003configured to, in case a first block is intra-predicted by directionalintra prediction, obtain a first predicted signal of the first block ofthe first picture by convolving the set of reference samples with afirst set of coefficients, and obtain a first reconstructed block of thefirst picture based on the first predicted signal; a second obtainingunit 2005 configured to, in case a second block of a second picture isintra-predicted by ALWIP, obtain a second predicted signal of the secondblock of the second picture by convolving the set of reference sampleswith a second set of coefficients, wherein the second set ofcoefficients comprises coefficients of a core matrix A of ALWIP, and thecoefficients of the core matrix A and the first set of coefficients havesame precision; upsampling the second predicted signal; and obtaining asecond reconstructed block of the second picture based on the upsampledsecond predicted signal.

FIG. 15 illustrates a decoder 30 based on the present disclosure. Thedecoder 30 of FIG. 15 comprises a preparing unit 3001 configured toprepare a set of reference samples; a first obtaining unit 3003configured to, in case a first block is intra-predicted by directionalintra prediction, obtain a first predicted signal of the first block ofthe first picture by convolving the set of reference samples with afirst set of coefficients, and obtain a first reconstructed block of thefirst picture based on the first predicted signal; a second obtainingunit (3005) configured to, in case a second block of a second picture isintra-predicted by ALWIP, obtain a second predicted signal of the secondblock of the second picture by convolving the set of reference sampleswith a second set of coefficients, wherein the second set ofcoefficients comprises coefficients of a core matrix A of ALWIP, and thecoefficients of the core matrix A and the first set of coefficients havesame precision; upsampling the second predicted signal; and obtaining asecond reconstructed block of the second picture based on the upsampledsecond predicted signal.

In the encoder 20 based on FIG. 14, and/or in the decoder 30 based onFIG. 15, the first and second obtaining units may be the same.

Mathematical Operators.

The mathematical operators used in this application are similar to thoseused in the C programming language. However, the results of integerdivision and arithmetic shift operations are defined more precisely, andadditional operations are defined, such as exponentiation andreal-valued division. Numbering and counting conventions generally beginfrom 0, e.g. ““the fir”t” is equivalent to the 0-th ““the seco”d” isequivalent to the 1-th, etc.

Arithmetic Operators.

The following arithmetic operators are defined as follows.

-   -   + Addition    -   − Subtraction (as a two-argument operator) or negation (as a        unary prefix operator)    -   Multiplication, including matrix multiplication    -   x^(y) Exponentiation. Specifies x to the power of y. In other        contexts, such notation is used for superscripting not intended        for interpretation as exponentiation.    -   / Integer division with truncation of the result toward zero.        For example, 7/4 and −7/−4 are truncated to 1 and −7/4 and 7/−4        are truncated to −1.    -   ÷ Used to denote division in mathematical equations where no        truncation or rounding is intended.

$\frac{x}{y}$

Used to denote division in mathematical equations where no truncation orrounding is intended.

$\begin{matrix}{\sum\limits_{i = x}^{y}{f(i)}} & \;\end{matrix}$

The summation of f(i) with i taking all integer values from x up to andincluding y.

-   -   x % y Modulus. Remainder of x divided by y, defined only for        integers x and y with x>=0 and y>0.

Logical operators.

The following logical operators are defined as follows.

-   -   x && y Boolean logica ““a”d” of x and y    -   x∥y Boolean logica ““ ”r” of x and y    -   ! Boolean logica ““n”t”    -   x? y: z If x is TRUE or not equal to 0, evaluates to the value        of y; otherwise, evaluates to the value of z.

Relational operators.

The following relational operators are defined as follows.

-   -   ≥ Greater than    -   >= Greater than or equal to    -   < Less than    -   <= Less than or equal to    -   == Equal to    -   != Not equal to

When a relational operator is applied to a syntax element or variablethat has been assigned the valu ““ ”a” (not applicable), the valu ““ ”a”is treated as a distinct value for the syntax element or variable. Thevalu ““ ”a” is considered not to be equal to any other value.

Bit-Wise Operators.

The following bit-wise operators are defined as follows.

-   -   & Bit-wis ““a”d”. When operating on integer arguments, operates        on a t‘o’s complement representation of the integer value. When        operating on a binary argument that contains fewer bits than        another argument, the shorter argument is extended by adding        more significant bits equal to 0.    -   | Bit-wis ““ ”r”. When operating on integer arguments, operates        on a t′o's complement representation of the integer value. When        operating on a binary argument that contains fewer bits than        another argument, the shorter argument is extended by adding        more significant bits equal to 0.    -   {circumflex over ( )} Bit-wis “ ” exclusive “r”. When operating        on integer arguments, operates on a t‘o’s complement        representation of the integer value. When operating on a binary        argument that contains fewer bits than another argument, the        shorter argument is extended by adding more significant bits        equal to 0.    -   x>>y Arithmetic right shift of a t‘o’s complement integer        representation of x by y binary digits. This function is defined        only for non-negative integer values of y. Bits shifted into the        most significant bits (MSBs) as a result of the right shift have        a value equal to the MSB of x prior to the shift operation.    -   x<<y Arithmetic left shift of a t‘o’s complement integer        representation of x by y binary digits. This function is defined        only for non-negative integer values of y. Bits shifted into the        least significant bits (LSBs) as a result of the left shift have        a value equal to 0.

Assignment Operators.

The following arithmetic operators are defined as follows.

-   -   = Assignment operator    -   ++ Increment, i.e., x++ is equivalent to x=x+1; when used in an        array index, evaluates to the value of the variable prior to the        increment operation.    -   −− Decrement, i.e., x−− is equivalent to x=−−1; when used in an        array index, evaluates to the value of the variable prior to the        decrement operation.    -   += Increment by amount specified, i.e., x+=3 is equivalent to        x=x+3, and x+=(−3) is equivalent to x=x+(−3).    -   −= Decrement by amount specified, i.e., x−=3 is equivalent to        x=−3, and x−=(−3) is equivalent to x=−−(−3).

Range Notation.

The following notation is used to specify a range of values.

-   -   x=y . . . z x takes on integer values starting from y to z,        inclusive, with x, y, and z being integer numbers and z being        greater than y.

Mathematical Functions.

The following mathematical functions are defined.

${{Abs}(x)} = \left\{ \begin{matrix}{x;} & {x>=0} \\{{- x};} & {x < 0}\end{matrix} \right.$

A sin(x) the trigonometric inverse sine function, operating on anargument x that is in the range of −1.0 to 1.0, inclusive, with anoutput value in the range of −π÷2 to n÷2, inclusive, in units of radians

-   -   Atan(x) the trigonometric inverse tangent function, operating on        an argument x, with an output value in the range of −π÷2 to n÷2,        inclusive, in units of radians

${A\tan 2\left( {y,\ x} \right)} = \left\{ \begin{matrix}{{A\;{\tan\ \left( \frac{y}{\;} \right)}}\ ;} & {x > 0} \\{{{A\;{\tan\ \left( \frac{y}{x} \right)}} + \pi}\ ;} & {{{{{x < 0}\ \&}\&}\ y}>=0} \\{{{A\;{\tan\ \left( \frac{y}{x} \right)}} + {- \pi}};} & {{{{{x < 0}\ \&}\&}\ y} < 0} \\{{+ \frac{\pi}{2}};} & {{x==0}\&\&{y>=0}} \\{{- \frac{\pi}{2}};} & {otherwise}\end{matrix} \right.$

-   -   Ceil(x) the smallest integer greater than or equal to x.    -   Clip1_(Y)(x)=Clip3(0, (1<<BitDepth_(Y)−−1, x)    -   Clip1_(C)(x)=Clip3(0, (1<<BitDepth_(C)−−1, x)

${Clip3\left( {x,y,z} \right)} = \left\{ \begin{matrix}{x;} & {z < x} \\{y;} & {z > y} \\{z;} & {otherwise}\end{matrix} \right.$

-   -   Cos(x) the trigonometric cosine function operating on an        argument x in units of radians.    -   Floor(x) the largest integer less than or equal to X.

${{GetCurrMsb}\left( {a,b,c,d} \right)} = \left\{ \begin{matrix}{{c + d}\ ;} & {{b - a}\ >={d/2}} \\{{{c - d};}\ } & {{a - b}\  > {d/2}} \\{c;} & {otherwise}\end{matrix} \right.$

-   -   Ln(x) the natural logarithm of x (the base-e logarithm, where e        is the natural logarithm base constant 2.718 281 828 . . . ).    -   Log 2(x) the base-2 logarithm of x.    -   Log 10(x) the base-10 logarithm of x.

$\begin{matrix}{{{Min}\left( {x,y} \right)} = \left\{ {{\begin{matrix}{{x;}\ } & {x<=y} \\{{y;}\ } & {x > y}\end{matrix}{{Max}\left( {x,y} \right)}} = \left\{ {{\begin{matrix}{x;} & {\ {x>=y}} \\{{y;}\ } & {x < y}\end{matrix}{{Round}(x)}} = {{{{Sign}(x)}*{{Floor}\left( {{{Abs}(x)} + {0.5}} \right)}{{Sign}(x)}} = \left\{ \begin{matrix}{{1;}\ } & {x > 0} \\{0\ ;} & {x==0} \\{{{- 1};}\ } & {x < 0}\end{matrix} \right.}} \right.} \right.} & \;\end{matrix}$

-   -   Sin(x) the trigonometric sine function operating on an argument        x in units of radians Sqrt(x)=√{square root over (x)}    -   Swap(x, y)=(y, x)    -   Tan(x) the trigonometric tangent function operating on an        argument x in units of radians

Order of Operation Precedence.

When an order of precedence in an expression is not indicated explicitlyby use of parentheses, the following rules apply. Operations of a higherprecedence are evaluated before any operation of a lower precedence.Operations of the same precedence are evaluated sequentially from leftto right.

Table 18 below specifies the precedence of operations from highest tolowest; a higher position in table 18 indicates a higher precedence.

For those operators that are also used in the C programming language,the order of precedence used in this Specification is the same as usedin the C programming language.

TABLE 18 Operation precedence from highest (at top of table) to lowest(at bottom of table)   operations (with operands x, y, and z)“ ″x” + ″“″x−“−″“ ″”x″“ ″”x″ (as a unary prefix operator) x^(y)«${\,^{``}x}*{»y}^{''}«{{\,^{\mspace{14mu}{``}}x}/{»y}^{''}}«{\,\mspace{14mu}}^{``}{x \div {»y}^{''}}{«\mspace{11mu}}^{``}\frac{x}{»}{\,^{''}»}\mspace{14mu}{\,^{``}x}\mspace{14mu}\%\mspace{14mu}{»y}^{''``}$″x +”y″“ ″− −”y″ (as a two-argument operator)“ ”$\sum\limits_{i = x}^{y}{{f(i)}^{''}``}$ ″x << ”y″“ ″x >> ”y″“ ″x < ”y″“″x <= ”y″“ ″x > ”y″“ ″x >= ”y″“ ″x = = ”y″“ ″x != ”y″“ ″x & ”y″“ ″x |”y″“ ″x && ”y″“ ″x | | ”y″“ ″x ? y:”z″“ ″x · ”y″“ ″x = ”y″“ ″x += ”y″“″x −=”y″

Text description of logical operations.

In the text, a statement of logical operations as would be describedmathematically in the following form.

-   -   if(condition 0)        -   statement 0    -   else if(condition 1)        -   statement 1    -   . . .    -   else /* informative remark on remaining condition */statement        -   n    -   may be described in the following manner:    -   . . . as follows / . . . the following applies:        -   If condition 0, statement 0        -   Otherwise, if condition 1, statement 1        -   . . .        -   Otherwise (informative remark on remaining condition),            statement n

Each “If . . . Otherwise, if . . . Otherwise, . . . ” statement in thetext is introduced with “ . . . as follows” or “ . . . the followingapplies” immediately followed by “If . . . ”. The last condition of the“If . . . Otherwise, if . . . Otherwise, . . . ” is always an“Otherwise, . . . ”. Interleaved “If . . . Otherwise, if . . .Otherwise, . . . ” statements can be identified by matching “ . . . asfollows” or “ . . . the following applies” with the ending “Otherwise, .. . ”.

In the text, a statement of logical operations as would be describedmathematically in the following form.

-   -   if(condition 0a && condition 0b)        -   statement 0    -   else if(condition 1a condition 1b)        -   statement 1    -   . . .    -   else        -   statement n    -   may be described in the following manner:    -   . . . as follows / . . . the following applies:        -   If all of the following conditions are true, statement 0:            -   condition 0a            -   condition 0b        -   Otherwise, if one or more of the following conditions are            true, statement 1:            -   condition 1a            -   condition 1b        -   . . .        -   Otherwise, statement n

In the text, a statement of logical operations as would be describedmathematically in the following form.

-   -   if(condition 0)        -   statement 0    -   if(condition 1)        -   statement 1            may be described in the following manner:    -   When condition 0, statement 0    -   When condition 1, statement 1

Although embodiments of the present disclosure have been primarilydescribed based on video coding, it should be noted that embodiments ofthe coding system 10, encoder 20 and decoder 30 (and correspondingly thesystem 10) and the other embodiments described herein may also beconfigured for still picture processing or coding, i.e. the processingor coding of an individual picture independent of any preceding orconsecutive picture as in video coding. In general only inter-predictionunits 244 (encoder) and 344 (decoder) may not be available in case thepicture processing coding is limited to a single picture 17. All otherfunctionalities (also referred to as tools or technologies) of the videoencoder 20 and video decoder 30 may equally be used for still pictureprocessing, e.g. residual calculation 204/304, transform 206,quantization 208, inverse quantization 210/310, (inverse) transform212/312, partitioning 262/362, intra-prediction 254/354, and/or loopfiltering 220, 320, and entropy coding 270 and entropy decoding 304.

Embodiments, e.g. of the encoder 20 and the decoder 30, and functionsdescribed herein, e.g. with reference to the encoder 20 and the decoder30, may be implemented in hardware, software, firmware, or anycombination thereof. If implemented in software, the functions may bestored on a computer-readable medium or transmitted over communicationmedia as one or more instructions or code and executed by ahardware-based processing unit. Computer-readable media may includecomputer-readable storage media, which corresponds to a tangible mediumsuch as data storage media, or communication media including any mediumthat facilitates transfer of a computer program from one place toanother, e.g., based on a communication protocol. In this manner,computer-readable media generally may correspond to (1) tangiblecomputer-readable storage media which is non-transitory or (2) acommunication medium such as a signal or carrier wave. Data storagemedia may be any available media that can be accessed by one or morecomputers or one or more processors to retrieve instructions, codeand/or data structures for implementation of the techniques described inthis disclosure. A computer program product may include acomputer-readable medium.

By way of example, and not limiting, such computer-readable storagemedia can comprise a random access memory (RAM), read only memory (ROM),electrically erasable programmable read only memory (EEPROM), compactdisk-read only memory (CD-ROM) or other optical disk storage, magneticdisk storage, or other magnetic storage devices, flash memory, or anyother medium that can be used to store desired program code in the formof instructions or data structures and that can be accessed by acomputer. Also, any connection is properly termed a computer-readablemedium. For example, if instructions are transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition of medium.It should be understood, however, that computer-readable storage mediaand data storage media do not include connections, carrier waves,signals, or other transitory media, but are instead directed tonon-transitory, tangible storage media. Disk and disc, as used herein,includes compact disc (CD), laser disc, optical disc, digital versatiledisc (DVD), floppy disk and Blu-ray disc, where disks usually reproducedata magnetically, while discs reproduce data optically with lasers.Combinations of the above should also be included within the scope ofcomputer-readable media.

Instructions may be executed by one or more processors, such as one ormore digital signal processors (DSPs), general purpose microprocessors,application specific integrated circuits (ASICs), field programmablelogic arrays (FPGAs), or other equivalent integrated or discrete logiccircuitry. Accordingly, the term “processor,” as used herein may referto any of the foregoing structure or any other structure suitable forimplementation of the techniques described herein. In addition, in someaspects, the functionality described herein may be provided withindedicated hardware and/or software modules configured for encoding anddecoding, or incorporated in a combined codec. Also, the techniquescould be fully implemented in one or more circuits or logic elements.

The techniques of this disclosure may be implemented in a wide varietyof devices or apparatuses, including a wireless handset, an integratedcircuit (IC) or a set of ICs (e.g., a chip set). Various components,modules, or units are described in this disclosure to emphasizefunctional aspects of devices configured to perform the disclosedtechniques, but do not necessarily require realization by differenthardware units. Rather, as described above, various units may becombined in a codec hardware unit or provided by a collection ofinteroperative hardware units, including one or more processors asdescribed above, in conjunction with suitable software and/or firmware.

What is claimed is:
 1. A method of intra prediction, comprising:preparing a set of reference samples; when a first intra prediction fora first block is directional intra prediction, performing the followingsteps: convolving the set of reference samples with a first set ofcoefficients to obtain a first predicted signal of the first block of afirst picture; obtaining a first reconstructed block of the firstpicture according to the first predicted signal; and when a second intraprediction of a second block is affine linear weighted intra prediction(ALWIP), performing the following steps: convolving the set of referencesamples with a second set of coefficients to obtain a second predictedsignal of the second block of a second picture, wherein the second setof coefficients comprise coefficients of a core matrix A of ALWIP, andwherein the coefficients of the core matrix A of ALWIP and the first setof coefficients have a same precision; upsampling the second predictedsignal; and obtaining a second reconstructed block of the second pictureaccording to the upsampled second predicted signal.
 2. The method ofclaim 1, wherein when the first intra prediction for the first block isdirectional intra prediction or when the second intra prediction of thesecond block is ALWIP, the method further comprises performing at leastone of following steps: adaptively defining the first set ofcoefficients per position of a first predicted sample of the set ofreference samples; or adaptively defining the second set of coefficientsper position of a second predicted sample of the set of referencesamples.
 3. The method of claim 1, wherein the coefficients of the corematrix A have a 6-bit precision such that 10-bit samples processing ofthe core matrix A fits in 16-bit arithmetic.
 4. The method of claim 1,further comprising: obtaining two lines of reconstructed neighboringsamples; deriving the set of reference samples based on the two lines ofreconstructed neighboring samples; obtaining an intra prediction modefrom a bitstream; obtaining a set of matrix-based intra prediction (MIP)coefficients based on the intra prediction mode, wherein a MIPcoefficient C_(MIP) of the set of MIP coefficients is obtained accordingto C_(MIP)=v_(sgn)·(q<<s), wherein q is a magnitude of the MIPcoefficient, wherein s is a left shift value, and wherein v_(sgn) is asign value of the MIP coefficient; obtaining a prediction block based onthe set of reference samples and the set of MIP coefficients; andobtaining a reconstructed picture based on the prediction block.
 5. Themethod of claim 4, further comprising obtaining the prediction blockfrom a matrix multiplication of the reference samples and the set of MIPcoefficients, wherein a multiplication operation in matrixmultiplication is performed with reduced bit depth by repositioningshift operation after multiplication and comprisesp·C_(MIP)=v_(sgn)·((p·q)<<s), where q is a magnitude of the MIPcoefficient, wherein s is a left shift value, wherein v_(sgn) is a signvalue of the MIP coefficient, wherein p is a reference sample, andwherein the p=bdry_(red) ^(top)[i] 0≤i<W or the p=bdry_(red) ^(left)[i],0≤i<H.
 6. The method of claim 5, wherein the magnitude of the MIPcoefficient is a 6-bit depth value.
 7. The method of claim 5, whereinthe left shift value is a 2-bit depth value.
 8. An apparatus,comprising: at least one memory configured to store programinstructions; and at least one processor coupled to the memory, whereinthe program instructions that when executed by the at least oneprocessor causes the apparatus to: prepare a set of reference samples;when a first intra prediction for a first block is directional intraprediction, the program instructions cause the apparatus to: convolvethe set of reference samples with a first set of coefficients to obtaina first predicted signal of the first block of a first picture; obtain afirst reconstructed block of the first picture according to the firstpredicted signal; and when a second intra prediction of a second blockis affine linear weighted intra prediction (ALWIP), the programinstructions cause the apparatus to: convolve the set of referencesamples with a second set of coefficients to obtain a second predictedsignal of the second block of a second picture, wherein the second setof coefficients comprise coefficients of a core matrix A of ALWIP, andwherein the coefficients of the core matrix A of ALWIP and the first setof coefficients have a same precision; upsample the second predictedsignal; and obtain a second reconstructed block of the second pictureaccording to the upsampled second predicted signal.
 9. The apparatus ofclaim 8, wherein when the first intra prediction for the first block isdirectional intra prediction or when the second intra prediction of thesecond block is ALWIP, the program instructions further cause theapparatus to perform at least one of: adaptively define the first set ofcoefficients per position of a first predicted sample of the set ofreference samples; or adaptively define the second set of coefficientsper position of a second predicted sample of the set of referencesamples.
 10. The apparatus of claim 8, wherein the coefficients of thecore matrix A have a 6-bit precision such that 10-bit samples processingof the core matrix A fits in 16-bit arithmetic.
 11. The apparatus ofclaim 8, wherein the program instructions further cause the apparatusto: obtain two lines of reconstructed neighboring samples; derive theset of reference samples based on the two lines of reconstructedneighboring samples; obtain an intra prediction mode from a bitstream;obtain a set of matrix-based intra prediction (MIP) coefficients basedon the intra prediction mode, wherein an MIP coefficient C_(MIP) of theset of MIP coefficients is obtained according to C_(MIP)=v_(sgn)·(q<<s)wherein q is a magnitude of the MIP coefficient, wherein s is a leftshift value, and wherein v_(sg)n is a sign value of the MIP coefficient;obtain a prediction block based on the set of reference samples and theset of MIP coefficients; and obtain a reconstructed picture based on theprediction block.
 12. The apparatus of claim 11, wherein the programinstructions further cause the apparatus to obtain the prediction blockfrom a matrix multiplication of the reference samples and the set of MIPcoefficients, wherein the multiplication operation in matrixmultiplication is performed with reduced bit depth by repositioningshift operation after multiplication and comprisesp·C_(MIP)=v_(sgn)·((p·q)<<s), wherein q is a magnitude of the MIPcoefficient, wherein s is a left shift value, wherein v_(sgn) is a signvalue of the MIP coefficient, wherein p is a reference sample, whereinthe p=bdry_(red) ^(top)[i] 0≤i<W or the p=bdry_(red) ^(left)[i], 0≤i<H,and wherein W is a width and H is a height of a block of thereconstructed neighboring samples.
 13. The apparatus of claim 11,wherein the magnitude of the MIP coefficient is a 6-bit depth value. 14.The apparatus of claim 11, wherein the left shift value is a 2-bit depthvalue.
 15. A computer program product comprising computer-executableinstructions stored on a non-transitory computer-readable storagemedium, that when executed by at least one processor, cause anintra-prediction apparatus to: prepare a set of reference samples; whena first intra prediction for a first block is directional intraprediction, the intra-prediction apparatus is configured to: convolvethe set of reference samples with a first set of coefficients to obtaina first predicted signal of the first block of a first picture; obtain afirst reconstructed block of the first picture according to the firstpredicted signal; and when a second intra prediction of a second blockis affine linear weighted intra prediction (ALWIP, the intra-predictionapparatus is configured to: convolve the set of reference samples with asecond set of coefficients to obtain a second predicted signal of thesecond block of a second picture, wherein the second set of coefficientscomprise coefficients of a core matrix A of ALWIP, and wherein thecoefficients of the core matrix A of ALWIP and the first set ofcoefficients have a same precision; upsample the second predictedsignal; and obtain a second reconstructed block of the second pictureaccording to the upsampled second predicted signal.
 16. The computerprogram product of claim 15, wherein when the first intra prediction forthe first block is directional intra prediction or when the second intraprediction of the second block is ALWIP, the computer-executableinstructions further cause the intra prediction apparatus to: obtain twolines of reconstructed neighboring samples; derive the set of referencesamples based on the two lines of reconstructed neighboring samples;obtain an intra prediction mode from a bitstream; obtain a set ofmatrix-based intra prediction (MIP) coefficients based on the intraprediction mode, wherein an MIP coefficient C_(MIP) of the set of MIPcoefficients is obtained according to C_(MIP)=v_(sgn)·(q<<s), wherein qis a magnitude of the MIP coefficient, wherein s is a left shift value,wherein v_(sgn) is a sign value of the MIP coefficient; obtain aprediction block based on the set of reference samples and the set ofMIP coefficients; and obtain a reconstructed picture based on theprediction block.
 17. The computer program product of claim 16, whereinthe computer-executable instructions further causes the intra predictionapparatus to obtain the prediction block from a matrix multiplication ofthe reference samples and the set of MIP coefficients, wherein themultiplication operation in matrix multiplication is performed withreduced bit depth by repositioning shift operation after multiplicationand comprises p·C_(MIP)=v_(sgn)·((p·q)<<s), where q is a magnitude ofthe MIP coefficient, wherein s is a left shift value, wherein v_(sgn) isa sign value of the MIP coefficient, wherein p is a reference sample,wherein the p=bdry_(red) ^(top)[i] 0≤i<W or the p=bdry_(red) ^(top)[i],0≤i<H, and wherein W is a width and H is a height of a block of thereconstructed neighboring samples.
 18. The computer program product ofclaim 16, wherein the magnitude of the MIP coefficient is a 6-bit depthvalue.
 19. The computer program product of claim 16, wherein the leftshift value is a 2-bit depth value.
 20. The computer program product ofclaim 15, wherein the computer-executable instructions further cause theintra prediction apparatus to perform at least one of: adaptively definethe first set of coefficients per position of a first predicted sampleof the set of reference samples; or adaptively define the second set ofcoefficients per position of a second predicted sample of the set ofreference samples.